Deconvolution-Based Algorithms for Deblurring PSP ...

51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition 07 - 10 January 2013, Grapevine (Dallas/Ft. Worth Region), Texas

AIAA 2013-0484

Deconvolution-Based Algorithms for Deblurring PSP Images of Rotating Surfaces James W. Gregory1, Kevin J. Disotell2, Di Peng3, and Thomas J. Juliano4 The Ohio State University, Columbus, Ohio, 43210 Jim Crafton5 Innovative Scientific Solutions, Inc., Dayton, Ohio, 45440 and

Downloaded by Di Peng on May 10, 2016 | http://arc.aiaa.org | DOI: 10.2514/6.2013-484

Narayanan M. Komerath6 Georgia Institute of Technology, Atlanta, Georgia, 30332

Blurring is a problem encountered when pressure-sensitive paint (PSP) is applied to rotating surfaces such as rotorcraft blades. The issue is particularly problematic near the leading and trailing edges of the blade: these are the regions where the impact of blurring is the most significant, yet they also contain the most valuable pressure information. Recent work has developed image deblurring techniques based on deconvolution of the image with a point-spread function (PSF) based on the known lifetime decay of PSP and rotation speed of the blade. This deblurring technique is effective in recovering information at the blade edges when the amount of blurring is not too high. However, the existing deblurring algorithm assumes rectilinear motion and uniform distribution of luminophore lifetime (i.e., constant pressure distribution). The objective of this work is to relax these assumptions by allowing for rotational blur and to assess the impact of strong pressure gradients. The new deblurring scheme is evaluated by experiments on a spinning disk with a known pressure field and a co-rotating, grazing nitrogen jet. The sensitivity of the deblurred results to various input parameters is evaluated, and recommendations for further algorithm development are provided.

Nomenclature A A a B B

= = = = =

calibration coefficient for PSP convolution matrix representing the blurring process (dimension N  N) speed of sound calibration coefficient for PSP blurred image (dimension m  n)

b e F

= = = =

discrete Fourier transform of image matrix B vector form of matrix B (dimension mn  1) random noise superimposed on image (dimension mn  1) two-dimensional discrete Fourier transform matrix

Bˆ

1

Assistant Professor, Dept. of Mechanical and Aerospace Engineering, 201 W. 19th Ave., AIAA Senior Member. NSF Graduate Research Fellow, Dept. of Mechanical and Aerospace Engineering, 201 W. 19th Ave., AIAA Student Member. 3 Ph.D. Candidate, Dept. of Mechanical and Aerospace Engineering, 201 W. 19th Ave., AIAA Student Member. 4 Postdoctoral Research Associate, Dept. of Mechanical and Aerospace Engineering, 201 W. 19 th Ave., AIAA Member. Now a National Research Council Postdoctoral Research Fellow at the Air Force Research Laboratory, Wright-Patterson AFB, OH. 5 Research Scientist, 2766 Indian Ripple Rd., AIAA Senior Member. 6 Professor, Daniel Guggenheim School of Aerospace Engineering, 270 Ferst Dr., AIAA Associate Fellow. 1 American Institute of Aeronautics and Astronautics 2

Copyright © 2013 by James W. Gregory. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


H I I I0 M m n N P r R r(Pr) s S Sn/Sx T t t U u V v X

= = = = = = = = = = = = = = = = = = = = = = =

discrete Fourier transform of the point spread function identity matrix PSP emission intensity as a function of time (arb.) initial PSP emission intensity (arb.) local rotational Mach number, r/a number of rows in matrix X number of columns in matrix X product of dimensions of matrix X; also, length of point spread function pressure (kPa) radial coordinate radius of spinning surface (m) recovery factor as a function of Prandtl number arc length coordinate (m) total arc length (m) noise-to-signal power ratio (NSR) temperature (K) time (s) time duration for the length of the point spread function (s) unitary matrix of dimension N  N left singular vectors (columns of matrix U) unitary matrix of dimension N  N right singular vectors (columns of matrix V) original, unblurred image (dimension m  n)

x x y

= = = =

discrete Fourier transform of image matrix X vector form of matrix X (dimension mn  1) rectilinear surface displacement during second exposure gate (m) distance from surface center of rotation to given spanwise location (m)

= = = = = = = = = =

regularization parameter change in quantity coefficients of regularization filter Lagrange multiplier for constrained filtering; also, ratio of specific heats for air (  = 1.4) eigenvalues of matrix A, dimension N  N polar angle coordinate (rad) diagonal matrix of singular values i singular values of matrix A, dimension N  N luminescent lifetime of PSP emission (s) surface rotation speed (1/s)

ˆ X

Greek



Δ

 







  

Subscripts exact = Gate A = Gate B = ∞ = i, j = naïve = ref = w =

quantity free of noise artifacts first integrated image in a lifetime decay second integrated image in a lifetime decay (relatively open-ended exposure) ambient condition indexing variables (i = 1, 2, …, N) and (j = 1, 2, …, N) solution obtained without noise regularization reference value wall value

Superscripts * = complex conjugate -1 = matrix inverse T = matrix transpose 2 American Institute of Aeronautics and Astronautics

I. Introduction


P

RESSURE-Sensitive Paint (PSP) is a diagnostic for non-intrusively measuring surface pressure distributions. The technique offers the advantages of high spatial resolution and low-cost, making it suitable for CFD validation and investigation of detailed flow structures that would otherwise be missed by conventional instrumentation such as pressure taps. PSP operates based on oxygen quenching of excited-state luminescence. A luminophore embedded in the PSP layer is elevated to a higher energy state through photon excitation, typically by UV or blue-wavelength illumination. The energy is then released through one of two primary mechanisms: interaction with oxygen molecules (oxygen quenching), or radiation of luminescence at a longer wavelength. Thus, the intensity of the emitted light from the paint is inversely proportional to the partial pressure of oxygen at the paint surface. The light emission is measured via an imaging device such as a CCD or CMOS camera. Bell et al.1 and Liu and Sullivan2 present comprehensive reviews of the PSP technique, its fundamental operating principle, and examples of applications. Recent developments in PSP technology have enabled high frequency response. The paint response is governed by the rate of oxygen diffusion within the paint layer, which is limited by the paint thickness and the diffusion coefficient of the binder. Conventional paint formulations have been limited to a frequency response on the order of 1 Hz. The paint response may be improved by decreasing the paint thickness, although this also decreases the emitted light and the resulting signal-to-noise ratio (Schairer3). A second approach is to improve the diffusivity by creating a porous binder structure. One common binder is based on a combination of a high percentage of ceramic particles (e.g., TiO2) with a small amount of polymer to form a polymer/ceramic PSP (Gregory et al.4). The resulting porous binder may be airbrushed onto the surface of interest, with a typical frequency response on the order of 5 kHz (Sugimoto et al.5). This paint formulation has recently been used for a study of resonant cavity acoustics (Gregory et al.6, Disotell and Gregory7), an investigation of the unsteady shock and wake shedding on a hemispherical dome (Fang et al.8), and on rotating surfaces such as helicopter blades (Juliano et al.9,10). Further details on the use of PSP for unsteady aerodynamics are given in the review by Gregory et al.4 Recent interest has focused on applying fast-response PSP to problems encountered in helicopter aerodynamics: unsteady loading on blades in forward flight (Wong et al.11-13, Watkins et al.14,15, Miyamoto et al.16), evaluation of the mechanisms of 2D compressible dynamic stall (Juliano et al.17, Jensen et al.18,19), resolution of unsteady flow structures over a rotating blade (Juliano et al.9,10, Disotell et al.20), and potential application to problems such as blade-vortex interaction and studies of 3D dynamic stall on rotating blades. Many of these rotorcraft situations involve application of PSP to a rotating blade. Further studies on rotating blades include the work of Yorita et al.21 and Klein22 for application of temperature-sensitive paint (TSP) or PSP to a rotating propeller blade. Initial application of fast-response PSP to rotating blades has involved phase-averaging techniques based on a once-per-revolution trigger signal (Gregory et al.23,24, Wong et al.11,12, Watkins et al.14). This acquisition technique is very limited when applied to rotorcraft, however, due to cycle-to-cycle variation in blade flapping, twist, and lead/lag angles inherent to an articulated, aeroelastic rotor. These cycle-to-cycle variations create a blurred wind-on image that is difficult to match with an arbitrary wind-off image. Another challenge inherent to rotorcraft testing with PSP in large facilities is the long working distance between the instrumentation and the test article. This requires a high-intensity illumination source, preferably a collimated source such as a high-energy pulsed laser. The difficulty in using a laser for intensity-based PSP is shot-to-shot variation in the spatial distribution of laser illumination due to speckle and the varying mode structure. Both of these challenges have led to the development of a single-shot, lifetime-based PSP method for rotorcraft (Gregory et al.25, Juliano et al.9,10, Wong et al.13, Watkins et al.15, Disotell et al.20). This technique is based on a pulsed laser for excitation, in order to provide sufficient excitation light at large working distances. The cycle-tocycle variations in blade position and shot-to-shot variation in illumination light field are overcome by acquiring data in the lifetime mode from a single lifetime decay curve originating from a single pulse of laser light. A windoff image is still necessary to correct for spatial variations in the paint response, but the self-referencing nature of the lifetime mode eliminates the problems of blade deflection between the wind-on and wind-off images. It is quite surprising that the technique is able to create full-well intensity images from only single pulses of excitation light – this is a byproduct of the high-energy laser illumination and highly-reflective nature of the polymer/ceramic PSP. Thus, high-quality PSP images can be obtained without any averaging of multiple images. Furthermore, the technique is capable of capturing transient pressure events that are characteristic to rotorcraft, without any phase averaging. This feature enables determination of RMS pressure fluctuations from an ensemble of single-shot images (Fang et al.8, Disotell et al.7,20). The bandwidth of the system is currently limited by available instrumentation (typical PIV cameras and pulsed lasers) to 15 Hz; however, work is underway to use the single-shot technique with

3 American Institute of Aeronautics and Astronautics


high-speed cameras and high-repetition rate pulsed lasers to extend the instrumentation bandwidth to 1 kHz (still within the typical PSP frequency response of about 5 kHz). The current implementation of the single-shot lifetime PSP technique is based on PIV cameras that have a short first exposure of controlled duration followed by a long, open-ended second gate inherent to the camera architecture (see Figure 120). The exposure duration of the second gate is limited by the readout time of the first gate image data from the CCD. The consequence of this is that a long-lifetime PSP will produce a blurred second gate image when applied to rotating helicopter blades. Initial approaches to helicopter aerodynamics with the single-shot technique were limited to short-lifetime, slow-response PSPs (such as Ru(bpp) in a polymer RTV binder; see Juliano et al.9). However, short-lifetime fast-response PSPs (e.g., Ru(bpp) in polymer/ceramic) had insufficient sensitivity to study the aerodynamic problems of interest on rotor blades. A PSP well-suited to measurement of unsteady pressures on rotating blades is PtTFPP in polymer/ceramic, although the lifetime is long enough such that blurring of the intensity in the second gate becomes an issue. This led to the development of first-order deblurring techniques (Juliano et al.10) based on deconvolution of the blurred image with a point spread function (PSF). Both Juliano et al.10 and Disotell et al.20 have effectively applied image deblurring to measurements of rotor blade pressure distributions. However, a rigorous assessment of the functionality, optimality, and limitations of the deconvolution scheme has not been performed. This work seeks to establish this knowledge and recommend areas for further development.

Figure 1: Notional timing diagram of the single-shot lifetime PSP technique.20 It is important to note that the deblurring techniques presented here are applicable to more problems than the specific situation that results from the architecture of the PIV camera used for lifetime PSP (a long, open-ended second exposure). Deblurring can be generally applied to any case where a long-exposure PSP image is desired on a rotating surface. For example, radiometric imaging of a spinning test article can benefit from deblurring techniques by removing a limit on exposure time and enabling higher signal-to-noise ratio. The schemes developed here are generally applicable to any rotational blurring motion with time-varying intensity of the imaged subject. This paper summarizes the development and functionality of deconvolution-based deblurring of PSP images of rotating blades. The current work extends Juliano et al.’s algorithm10 by applying the deconvolution to more general blade motions. Furthermore, the new algorithm is evaluated based on single-shot PSP measurements of a rotating disk. These experiments and analysis yield insight into the capabilities and structural limitations of deconvolution-based deblurring schemes.

II. Background on Image Deblurring Motion blur is a commonly-encountered problem in imaging, particularly when long exposure times are required in low-light settings. Thus, it is a well-studied problem that has a strong theoretical foundation. In this section a brief overview of image deblurring theory and approaches will be presented (loosely following the discussion of Hansen et al.26), followed by details on the particular problem of rotational blur. A more detailed treatment of image deblurring is provided by Hansen et al.26, Hansen27, Gonzalez and Woods28, and Nagy et al.29 4 American Institute of Aeronautics and Astronautics


A. Inverse Problems and Noise Amplification Image blurring is a part of a class of inverse problems: we wish to know what sharp image would produce a given blurred image with a (known or unknown) blurring model. Inverse problems are, in turn, part of a class of illposed problems in mathematics. One significant characteristic of an ill-posed problem is that the solution is very sensitive to perturbations and error in the input data, leading to the need for regularization (i.e., filtering). 27 A model for the blurred image resulting from the original image may be given by b  Ax , (1) where b and x are the vectorized forms of the images B and X, respectively, with each image having dimension m  n and each vector is N = mn elements long. A is the convolution matrix that represents the blurring process, with dimension N  N. It tends to be a sparse matrix, with each column containing a vectorized form of the point spread function corresponding to a given pixel in X. The PSF is a small matrix that represents the distribution of intenstity from a single point source at the center of the PSF. A point spread function having a center pixel with value of unity surrounded by an array of zero values would have no impact on the original image x (consider the vectorization of this notional PSF and arrangement into the blurring matrix A; the result is A = I, the identity matrix). Two examples of point spread functions and their impact on an image are shown in Figure 2. A defocusing PSF is a disk of uniform intensity and a given radius (8.5 pixels in the case shown in Figure 2(d)), which results in the blurred image shown in Figure 2(b). Similarly, a motion blur PSF is a line of high-intensity pixels oriented in the direction of the blur (15 pixels long in the case shown in Figure 2(e)), resulting in the blurred image in Figure 2(c). Both blurred images were created by convolving the appropriate PSF with the original image (Figure 2(a)) using periodic boundary conditions.

(a)

(b)

(c)

(d) (e) Figure 2: Blurring examples. The original image (a) of resolution 340  340 pixels is blurred by the disk PSF with 51  51 pixels resolution (d), resulting in (b). The motion blur PSF in (e) results in the blurred image (c). If one has specific knowledge of the point spread function, then it may be possible to infer the original image from the blurred image. It may be tempting to deconvolve the PSF with the blurred image by

x naïve  A 1b  A 1 Ax ,

(2)

however this will not yield acceptable results if there is any appreciable noise in the image. For reasons that will be shown momentarily, the naïve solution is dominated by noise since high-frequency noise is amplified more than the low-frequency image information in the deconvolution process. Results from an attempt to deblur a noisy form of the images shown in Figure 2 without regularizing the noise are illustrated in Figure 3. Here, noise with variance of 110-4 (representative noise level of typical imagers) was added to the original image before deblurring. Clearly the noise dominates the solution and the original image cannot be effectively reconstructed via the naïve solution. It should be noted, however, that Eq. 2 is capable of reconstructing the original image for both cases presented in Figure 2 as long as no noise is present. The superposition of noise onto the blurred image is an inevitable artifact of the imaging process (shot noise, readout noise, discretization error, etc.). This may be represented by

b  b exact  e , where e represents the additional random noise. Thus, Eq. 2 can be re-written as 5 American Institute of Aeronautics and Astronautics

(3)

x naïve  A 1b  A 1b exact  A 1e  x  A 1e ,

(4)

-1

which indicates that the magnitude of the inverted noise term (A e) depends on the nature of the inverse of the blurring matrix A.


(a) (b) Figure 3: Deblurring examples with no regularization of noise. The original image of Figure 2(a) with added noise of var=110-4 is deblurred by the naïve solution for the disk PSF (a) and the motion blur PSF (b). The reason that the noise is amplified becomes apparent when considering the singular value decomposition (SVD) of A (briefly reviewed here in order to establish nomenclature). The SVD may be expressed as

A  UΣVT ,

(5)

where the matrices U and V are each orthogonal such that

UT U  I and V T V  I .

(6) The matrix  is a diagonal matrix, =diag(i), such that the singular values i are nonnegative and nonincreasing (1  1  …  N  0). The condition number of A, expressed as cond(A) = 1/N, is very large since the singular values decay to very low values near zero. This implies that the solution to the blurring problem will be very sensitive to perturbations such as noise and rounding errors. The columns ui of U are referred to as left singular vectors, while the columns vi of V are referred to as right singular vectors. Due to Eq. (6), uiTuj = 0 if i  j and viTvj = 0 if i  j. Now, if all singular values are assumed to be positive, the inverse of the blurring matrix can be given by

A 1  VΣ -1UT .

(7) Since  is a diagonal matrix, the invserse  is also diagonal with elements 1/i. At this juncture, it is important to highlight that the basis vectors vi of V (i.e., the left singular vectors) represent the spectral content – each successive basis vector is characterized by a higher spatial frequency. Thus, the singular value decomposition of A can be said to represent the spectral content. The matrices A and A-1 can also be expressed as26 -1

A  UΣV T T  1   v1      u1  u N       N   v TN  ,  u1 1 v1T    u N  N v TN

(8)

N

   i u i v Ti i 1

and similarly, N

A 1  VΣ -1U T   i 1

1

i

v i uTi .

(9)

Returning to Eq. 4, the inverted noise term may now be expressed as N

uTi e

i 1

i

A 1e  VΣ -1U T e  

vi .

(10)

using SVD. This last expression (Eq. 10) provides insight into the fundamental reason for noise amplification in the deblurring process. The error coefficients (uiT e) tend to be small and relatively constant in value. However, as was 6 American Institute of Aeronautics and Astronautics

shown earlier, the singular values (i) rapidly diminish and become very small as i increases. These small values correspond to the higher-frequency left singular vectors (vi). Thus, the noise associated with high frequencies is amplified in the deconvolution process, leading to results as shown in Figure 3(a) and (b). If singular value decomposition is used as a technique for solving the linear ill-posed inverse problem, certain filtering strategies may be implemented to regularize the solution. A construct for describing these SVD filtering schemes is given by N

x  A 1b  VΣ -1UT b   i i 1

uTi b

i

vi .

(11)

The coefficients i may be used to effectively filter out the high-frequency noise terms that tend to be amplified. Thus, one filtering scheme is

1, 1  i  k , 0, k  i  N

i  

(12)


which effectively truncates the higher-frequency terms beyond element k in the SVD (referred to as truncated SVD, or TSVD). Another filtering scheme, attributed to Tikhonov, has coefficients

i 

 i2 ,  i2   2

(13)

where  is the regularization parameter (the higher the value of , the more filtering there is). This effectively serves as a low-pass filter with a more gradual cutoff than TSVD. B. Spectral Decomposition and Fast Deblurring Schemes Fast deconvolution schemes have been developed in order to efficiently handle images of appreciable size. If the matrix A is of the form “block circulant with circulant blocks” (as is true for a spatially invariant PSF applied to an image using periodic boundary conditions), then is can be spectrally decomposed as 26 (14) A  F* ΛF . Here F is the two-dimensional discrete Fourier transform (DFT) matrix, and F* is its complex conjugate. Conveniently, the spectrum  (eigenvalues of A) can be computed by taking the fast Fourier transform (FFT) of the PSF (recall that each column of A is a shifted, vectorized form of the PSF). This property is highly advantageous for efficient computations, since the large A matrix need not be explicitly computed. Thus, the Fourier decomposition analogous to Eq. 2 is given by

x naïve  A 1b  F* Λ 1Fb .

(15)

In the frequency domain, Eq. 15 can be expressed as

ˆ ˆ B, X H

(16)

ˆ 1 ˆ H* H2 ˆ  X B   2   B . 2  H   S n S x   H H   S n S x 

(17)

ˆ and Bˆ are the discrete Fourier transforms of the images X and B, and H is the DFT of the point spread where X function. The DFT and its complex conjugate can be easily and efficiently computed via FFT algorithms (e.g., the fft2 and ifft2 functions in MATLAB). A short block of MATLAB code that is equivalent to the inverse Fourier transform of Eq. 16 is given by:26 H = fft2( circshift(PSF, 1 – center) ); X = real( ifft2( fft2(B) ./ H ) ); (X is the deblurred image, B is the blurred image, and PSF is the point spread function; the circshift command is used to shift the center of the point spread function to the corner of the matrix; the real value of the inverse DFT is taken in order to ignore spurious imaginary values of the complex computations, since PSF and B are realvalued). Equation 15 was used to generate the naïve solutions presented in Figure 3; thus, this form of the spectral decomposition does not include regularization to address noise. Gonzalez and Woods presented a form of the Fourier transform that includes filtering:28



Here the term Sn/Sx represents the noise-to-signal power ratio, which may need to be estimated for a given image. (Note that if the noise-to-signal ratio is zero, then Eq. 17 reduces to Eq. 16, giving the naïve solution). If =1, then the transfer function in brackets in Eq. 17 is referred to as the Wiener filter. An accurate estimate of the noise-tosignal ratio allows for regularization of the noise, effectively acting as a filter cutoff frequency. Figure 4 shows results from application of the FFT with Wiener filtering (Eq. 17) to deblurring of the degraded images shown in Figure 2, with a noise-to-signal estimate based on the known added noise variance relative to the variance of the original image. It is clear that the reconstruction based on regularization techniques is far superior to the naïve solution (Figure 3) for this level of noise. The deconvolution scheme represented by Eq. 17 is implemented in MATLAB Image Processing Toolbox as the function deconvwnr. A similar block of MATLAB code could be given as (NSR is the noise-to-signal ratio): H = fft2( circshift(PSF, 1 – center) ); X = real( ifft2( conj(H).* fft2(B) ./ ( H.^2 + NSR ) ) ); .

(b) (a) Figure 4: Deblurring examples with noise regularization. The original image of Figure 2(a) with added noise of var=110-4 is deblurred by the Fast-Fourier Transform scheme with Wiener filtering for the disk PSF (a) and the motion blur PSF (b). C. Estimation of the PSF The preceeding discussion assumes that the point spread function is spatially invariant. That is, every pixel in the image X is blurred by the same amount and in the same manner. The PSF may be determined in a variety of ways. For example, if one is imaging a star field through a telescope and recorded on a camera via long exposure, then the motion of the star images may be determined knowing the rotation rate of the Earth, as well as the location, orientation, and field of view of the telescope.30 Another example of recent work in estimating the PSF is with blurry images resulting from camera shake. Normally, the precise motion of the photographer's hand during an exposure would not necessarily be known. However, modern schemes use a portion of the image with distinct features (say, a sign with letters) can be used to estimate a PSF. 32,33 Or, even more recently, researchers have used the accelerometer and gyroscope information captured during a camera exposure on modern smartphones to generate a PSF.34 If the PSF is not known a priori, then an added layer of complexity in the deblurring process is introduced, as the PSF must be estimated. If there is no external information on which to base the estimate of the PSF, then the process reverts to blind deconvolution where the PSF must be estimated and applied in a recursive manner.35 D. Rotational Blur The stipulation of a spatially-invariant blur is not generally applicable, however. Any rotational motion of the camera or of the imaged object results in a spatially variant blur – the amount and direction of blur is a function of a pixel’s location relative to the center of rotation. This particular problem arises in many situations including machine vision, astronomy, camera shake, camera zoom, and imaging of rotating blades. There have been several approaches proposed for handling rotational blur. The most straightforward approach involves mapping the image from Cartesian to polar coordinates relative to the image’s center of rotation. 36-41 Motion in the polar coordinate system is uniform, leading to definition of a spatially-invariant PSF. Once the image in polar coordinates has been deblurred, it may be re-mapped back to Cartesian coordinates. This approach has proven to be effective, although there are challenges with pixel drop-out in the two-way interpolation process and potential loss of resolution. A second approach to the rotational blur problem is to employ an array of spatially variant point spread functions.30-31,35,41-43 Algorithms using this approach are generally more complicated and require more computational time. The structure of the convolution matrix (A) becomes complex and more ill-conditioned. However, this approach has been successfully used for problems such as deblurring long-time-exposure images 8 American Institute of Aeronautics and Astronautics


acquired by telescope, and a set of MATLAB functions (“RestoreTools” 29) has been developed that incorporates the capability to handle spatially-variant PSFs. A third approach based on a kernel-free model has recently been proposed.44 This concept involves an intuitive approach to defining a forward model, where a sharp image is incrementally rotated and integrated to form a blurred image. This forward model can then be used in an adjoint manner with an iterative scheme to deblur an image. This model is attractive due to its intuitive approach, although it is computationally demanding. E. Deblurring of Rotating PSP Images Image deblurring based on deconvolution of the blurry image with a point-spread function was first developed for PSP on rotorcraft by Juliano et al,10 and has been implemented by Watkins et al.15 and Disotell et al.20 The source of blurring is the rotation of a painted blade within the long second gate of a double-exposure frame-transfer camera used in lifetime mode, where the paint emission exhibits a long lifetime decay. The key to this method is in determining an accurate estimate of the point-spread function. Fortunately, most of the parameters that dictate the blurring are well-known. The rotation rate of the rotor blade is known via the 1/rev signal from a shaft encoder. The blade geometry is known, as well as the camera position, orientation, and optics parameters. Furthermore, the local lifetime of the PSP is known to first order. The following summarizes Juliano et al.’s development of the technique.10 Based on the known properties of luminescent lifetime and blade rotation, a point-spread function is defined as follows. The paint emission is assumed to follow a single exponential decay, given as

I  I 0 e t / .

(18)

Blade movement is considered to be solid body rotation, where the movement as a function of span is given by (19) x  yt , which assumes that the motion at a given spanwise location y is rectilinear. The paint lifetime and blade motion are combined to form a one-dimensional point-spread function,

I  I 0 e  x / y .

(20)

This PSF is then deconvolved with the image of the blade on a column-by-column basis, assuming that the image has been rotated such that the blade leading edge is parallel to the image rows. Thus, rectilinear motion is an assumption inherent to the current implementation of the technique. Furthermore, the current configuration of the deblurring scheme assumes a constant, average value of luminescent lifetime ( ). Image deblurring operations are performed in the MATLAB Image Processing Toolbox using the deconvwnr function (based on Eq. 17).

III. Experimental Setup A rotating disk has been set up in order to experimentally evaluate the image deblurring without the impact of a pressure gradient (see Figure 5). A 203-mm (8-inch) diameter steel disk was spun on a 2.24-kW (3 hp) electric motor. The entire disk was painted with a black base coat followed by the polymer/ceramic binder,4 with a wedgeshaped strip (~35 included angle) of PtTFPP luminophore applied as an overspray. The entire disk was painted with the binder material for an axisymmetric surface finish, such that flow disturbances would not be introduced by any edges of the PSP. A wedge-shaped sensing area with applied luminophore was painted such that the ratio of the local tangential speed ( y) to the chordwise thickness of the stripe is constant, giving a constant blurring time across the span of the disk. The disk operation speed ranged from 134 Hz (8,040 rpm) up to 269 Hz (16,140 rpm), giving a maximum tip speed of 171.6 m/s in the counter-clockwise direction (as viewed by the camera). The PSP was illuminated by a pulsed Nd:YAG PIV laser with approximately 100 mJ/pulse (200 mJ/pulse if both cavities are fired simultaneously) at a 15-Hz repetition rate, fed through a negative lens and a diffuser for volume illumination. A 14bit CCD camera (Cooke Corp. pco.1600) with interline-transfer chip was used for PSP interrogation (recall that the second frame is open-ended with an exposure that cannot be set, leading to the image blurring problem in the second gate). The laser and camera were operated in single-shot lifetime mode, as described elsewhere. 7-10, 20 ,25 Timing of the laser and camera with the disk rotation was established by locking on to a 1/rev signal from an optical shaft encoder fed through a pulse/delay generator. A further addition to this setup involves a nitrogen jet spraying tangentially across the disk surface, in order to induce a sharp-edged gradient in local oxygen concentration (thus, emitted intensity). This feature setup allows for the evaluation of the deblurring algorithm applied to discontinuous lifetime decay time constants. The nitrogen jet is produced by supplying nitrogen from a pressurized cylinder through a rotary union to a plenum at the disk hub (in the rotary frame of reference). The rotating plenum supplies a small nozzle that injects nitrogen in the radial outward direction. 9 American Institute of Aeronautics and Astronautics


Figure 5: Experimental setup for the spinning disk.

IV. Deblurring Images of Rotating PSP in Lifetime Mode A. Algorithm Revision The present work seeks to improve upon the initial deblurring scheme 10 and perform a robust assessment of the technique’s capabilities. First, the algorithm will be generalized such that the assumption of rectilinear motion is dropped. Blade rotation along an arbitrarily long arc can now be considered via transformation of the image coordinate system. This modification enables the technique to operate on images with a long lifetime ( ) or high rotational speed ( ). Furthermore, this development obviates the need to rotate the image to align the direction of motion with the pixel columns of the image. A transformation from Cartesian to polar coordinates based on the work of Ribarić et al.36 was implemented. The essential elements of the transformation are a stipulation that the resolution of the polar coordinates must be at least as high as that of the original image, and that bilinear interpolation be used to map intensity values from one coordinate system to the other. For the work on the spinning disk presented here a radial resolution of 495 pixels/R (r = 0.002/pixel) and an angular resolution of 10 pixels/degree ( = 0.1/pixel) was selected, providing a higher resolution grid than the original data set. An example of the results from this transformation are shown in Figure 6. A convenient byproduct of this coordinate mapping is that radial or circumferential profiles of the PSP intensity or intensity ratio become trivial to aquire from the polar coordinate image. The key consequence of this coordinate mapping is that the circumferential blur (assumed to be rectilinear in Eq. 19) is now one-dimensional, as given by   t . (21) Thus, the point spread function in polar coordinates becomes

I  I 0e  /   , 10 American Institute of Aeronautics and Astronautics

(22)


which is a spatially invariant blur since it is not a function of r or . A significant consequence of this construct is that the deconvolution may be applied to the entire image in one pass (Eq. 17), rather than applying the deconvolution on a column-by-column basis in the previous approach.10 This leads to substantial savings in computational time, with the new algorithm requiring only on the order of several seconds on a desktop PC to read 600  800 pixel resolution images, map to polar coordinates, deblur, and map back to Cartesian coordinates. A typical point spread function used in this work is shown in Figure 7 for a rotational speed of 269 Hz (1690 rad/s), a characteristic lifetime time constant of 9.3 s, and a length of N = 10 lifetimes. The one-dimensional PSF is normalized by the integral of Eq. 22 over the length of the PSF (N = 10 in this case).

(a) (b) Figure 6: Coordinate mapping from (a) Cartesian image coordinates to (b) polar coordinates. Disk rotation direction is indicated by the white arrows, with the leading edge at the bottom of (a) and at the right of (b).

Figure 7: Normalized point spread function (Eq. 22) with  = 1690 rad/s,  = 9.3 s, and N = 10. B. Questions on Algorithm Performance Even though the deblurring technique has been applied to rotorcraft PSP in several instances, 10,15,20 there has not yet been published a robust assessment of the algorithm performance. Several questions remain unaddressed at this juncture. First, how well does the new algorithm (with mapping to polar coordinates) handle an arbitrarily long lifetime blur? In particular, for PSP, how well can deblurring restore the known solution of zero pressure gradient in the circumferential direction? This will be evaluated by applying the revised algorithm to experimental data from a spinning disk at high rotary speed. The results will be examined in detail to assess deblurring performance. Second, what is the impact of imager noise on the solution? Is the noise appreciably amplified, as the theory suggests? 11 American Institute of Aeronautics and Astronautics

Correspondingly, how well does regularization in the deblurring process filter the noise? This will be assessed by applying various levels of additive noise to the baseline images and examining the deblurred results. The impact of Wiener filtering via the regularization parameter (the noise-to-signal ratio, Sn/Sx, in Eq. 17) will be evaluated. Third, how well can this algorithm with the assumption of constant luminophore lifetime address strong pressure gradients? If the current algorithm is insufficient, then this could provide motivation for development of deblurring based on a spatially-variant PSF. The need for this will be assessed by images of the grazing nitrogen jet on the spinning disk. The nitrogen jet creates a very strong intensity gradient (likely greater than any gradient produced by a pressure jump), which will establish a worst-case scenario for the deblurring algorithm. These questions are addressed in the results section, following an initial characterization of the PSP formulation.


V. Results A. Paint Characterization For the purposes of this study, the specific charactaristics of the PSP formulation (PtTFPP on polymer/ceramic) needed to be evaluated. These characteristics include the pressure and temperature sensitivities, along with the lifetime time constant () as a function of pressure. The values of these parameters are typical for this paint formulation, however they have not been clearly documented in the literature. Furthermore, the pressure and temperature sensitivity is known to vary based on the specific details of the lifetime timing setup used in the experiment. Thus, the results are presented here and serve as critical input parameters for the following work. The pressure and temperature calibrations were carried out in an enclosed calibration chamber with pressure and temperature control. The same instrumentation and timing details as used in the spinning disk setup were employed for the calibrations. The pressure range was 41.4 to 165.5 kPa in steps of 20.7 kPa (Pref = 103.5 kPa, Tref = 298 K), and the temperature range was 293 to 313 K in steps of 2 K (Tref = 303 K, Pref = 103.5 kPa). The pressure calibration for the lifetime technique still requires a wind-off reference, despite the self-referencing nature of the ratio of two gated intensity values from one decay curve (Figure 1). Thus, the pressure calibration may be expressed as the ratio of ratios,

I Gate B I Gate A ref I Gate B I Gate A 

 AT   BT 

P , Pref

(23)

where the calibration coefficients A and B are functions of temperature. Ideally, the timing values between Gate A and Gate B should be set such that Gate B has all of the pressure sensitivity and Gate A is relatively constant. The results from the pressure and temperature calibrations are presented in Figure 8.

(a) (b) Figure 8: Pressure (a) and Temperature (b) calibration curves for polymer/ceramic PSP with PtTFPP. The lifetime decay calibrations were conducted in the same calibration chamber, across the same range of pressures, but with a photomutiplier tube (PMT) as the photodetector. The intensity time histories were recorded on a digital oscilloscope with a sampling rate of 100 MHz, and each trace is the average of 50 lifetime decay curves (see Figure 9). The logarithm of each decay curve was plotted as a function of time (Figure 9b), with a linear fit applied in order to determine the time constant ( ) for each pressure. The lifetime time constants as a function of pressure are plotted in normalized and dimensional form in Figure 10, where the reference conditions are ref = 9.59 s and Pref = 103.5 kPa. The data presented in Figure 10(b) is particularly useful for any iterative scheme with a 12 American Institute of Aeronautics and Astronautics


spatially-variant point spread function. In that scenario, the algorithm would need to recursively deblur images and determine the surface pressure based on an initial guess for , and update the initial guess based on the pressure/lifetime data presented here.

(a) (b) Figure 9: Measured lifetime decay curves on linear (a) and semi-log (b) axes. Each black line in (b) represents a curve fit for that pressure.

(a) Figure 10: Lifetime calibration values in normalized (a) and dimensional (b) form.

(b)

B. Deblurring Performance at High Rotational Speeds The initial assessment of the new deblurring algorithm was performed by deblurring experimental data from the spinning disk operated at 269 Hz. This condition was selected as the highest possible rotation speed that could be safely and reliably established by our test setup. Deblurring of the images was conducted with Eq. 17, with an estimate of zero noise for regularization parameter (Sn/Sx = 0). The PSF for this case is the same one that is shown in Figure 7, for  = 1690 rad/s (269 Hz),  = 9.3 s, and N = 10. With the camera viewing from nearly directly overhead, wind-on images from the open-ended Gate B are shown in Figure 11 (displayed in Cartesian coordinates). The leading edge is at the bottom edge, with the PSP region moving downward and to the right. The left images, (a) and (c), show the effects of blurring on the blade edge and the registration markers. Image (a) clearly has extensive blurring that makes the marker much more difficult to pinpoint. Images (b) and (d) of Figure 11, with the colorbar truncated to limit the dynamic range, clearly show the full extent of blurring from the leading edge. The intensity is smeared over a distance of 20 to 30 pixels (on the order of 10% of the arc length chord). Thus, this amount of blurring would lead to serious complications in a test with a rotor blade or propeller, where the suction peak at the leading edge could be completely obscured by the blur pattern. The upshot is that the deblurring scheme appears to work exceptionally well, despite the strong circumferential blur. The edges of the images in Figure 11 (b) and (d) appear to be very sharp (within 1 pixel), despite going through two coordinate transformations and the deconvolution process. 13 American Institute of Aeronautics and Astronautics


Another view of the deblurring results is shown by the chordwise intensity profiles in Figure 12. These profiles were taken from the polar coordinates image at a radial location of r/R = 0.95 and normalized by the total arc length of the PSP at that location. The wind-on Gate B blurred intensity data is slightly amplified at the leading edge (relative to the deblurred solution), while the blurred data is significantly attenuated at the trailing edge. This blur pattern is what would be expected for a rotating object with an exponential decay in intensity, and is similar to the patterns observed by Juliano et al.10 Another interesting feature is the smooth contour of the blurred profile relative to the On A profile (which has a very short exposure time and is relatively immune to blur). The blurring process effectively acts as a smoothing filter to even out the spatial intensity variations (due to laser speckle, paint inhomogeneities, etc.). The deblurred On B profile has slightly more noise than either of the other profiles. This is consistent with our expectation that the deconvolution process amplifies high-frequency noise in the signal. What is surprising, however, is that the level of noise in this single-exposure image (no averaging) is small enough that amplification of that noise by deconvolution does not dominate the solution as it did in Figure 3. This provides some initial indication that no regularization may be needed for this work; the effect of regularization will be addressed shortly. A final observation regarding the deblurred On B profile in Figure 12 is that amplified spikes in the intensity profile emerge at the leading and trailing edges. The spike at the leading edge occurs just outside the domain of interest, but the trailing edge spike remains within the PSP domain and is problematic. This excursion from the expected profile is likely due to the Gibbs effect, which is an artifact of including higher-frequency terms in the Fourier transform. Thus, it is consistent that ringing oscillations in the signal response would occur at the leading and trailing edges, where the most significant high-frequency content is present.

(a)

(b)

(c) (d) Figure 11: Gate B wind on images of the tip corner of the painted wedge spinning at 269 Hz: original blurred images (a) and (b); deblurred images (c) and (d). Images (b) and (d) have a truncated colorbar to more clearly show exponential decay of the blur pattern in (b), and the removal of the blur in (d). The sensitivity of the solution to the various input parameters to the PSF can be evaluated. Rotation speed is known to high accuracy in most cases, so it is not considered here. The luminescence lifetime ( ) was varied over a range of 15% relative to the baseline value, but was found to have a negligible impact on the deblurred profile relative to the noise. The length of the PSF (N) in the circumferential direction is a parameter that can be expected 14 American Institute of Aeronautics and Astronautics


to have an impact on the solution. If it is too short, then the lifetime decay curve in the PSF will be truncated and not enough of the blurred light will be reconstructed. If it is too long, there is a chance that the very low-level tail of the exponential function will amplify the noise inherent to the image (since the 2D-FFT of the PSF appears in the denominator of Eq. 17). Figure 13 shows the variation of the deblurred, wind-on Gate B profiles for various lengths of the PSF. The most substantial impact is at the edges, where truncation of the PSF leads to a reduction in the sharp edges and trending towards the blurred solution. There does not seem to be much difference in the overall structure of the profiles beyond a PSF distance of N = 4, which is not surprising since over 98% of the signal occurs within the first 4 of the exponential decay curve. There may be a small amount of noise amplification for the longer PSFs, but it does not appear to be substantial.

Figure 12: Chordwise intensity profiles of the wind on images, taken at r/R = 0.95. Note the slightly increased noise on the deblurred profile relative to the blurred profile.

Figure 13: Effect of varying the size of the PSF from N = 1 to N = 10 long; chordwise intensity profiles of wind on Gate B images at r/R = 0.95.

With the successful deblurring of the wind-on Gate B images, the question arises as to whether the shortexposure Gate A images require deblurring. These exposures tend to be very short (6 s in this case, or 0.64), but that is still long enough for a blur pattern of nearly 6 pixels (~2% chord) to occur at this rotational speed and camera resolution. An attempt was made to deblur the wind-on Gate A image, with the results shown in Figure 14. The “blurred” image in (a) looks fairly sharp, but close inspection reveals a few pixels of blur around each registration marker. The deblurred image (b) effectively sharpens the edges, but also introduces significant Gibbs ringing that extends for about 10% chord at the trailing edge (left side of the image). Due to the significant high-frequency ringing that emerged in the image, this effort was abandoned. As will be shown, suitably accurate results are obtained without deblurring of Gate A.

(a) (b) Figure 14: Wind-on Gate A images without (a) and with (b) deblurring. Note the sharper edges on registration markers in (b), but also the Gibbs effect ringing near all features with high spatial frequency content (edges). 15 American Institute of Aeronautics and Astronautics

The ratio of ratios (left-hand side of Eq. 23) resulting from the registered images is shown in Figure 15 in Cartesian coordinates. The same registration scheme (based on the same control points) has been applied to both images; the only difference is that the ratio of ratios in Figure 15(a) is based upon the original blurred image, while the ratio of ratios in (b) results from the deblurred wind-on Gate B image. In both cases, it is evident that there is a strong radial gradient in the intensity ratio. However, a spinning disk has no boundary condition by which it can sustain a radial pressure gradient. Thus, this intensity gradient is likely due to the temperature sensitivity of the PSP. There is an expected radial temperature gradient, which can be expressed as the adiabatic wall recovery temperature:

   1 2  Tw  T 1  r ( Pr ) M  .  2   

(23)


Even though a steel disk is typically not considered adiabatic, the thermal properties of the polymer/ceramic PSP formulation are a good insulator.45 Thus, the adiabatic wall recovery temperature is a reasonable explanation for this radial intensity gradient; indeed, the predicted tip wall temperature coupled with the temperature sensitivity of polymer/ceramic PSP yields a greater change in intensity than what the PSP indicates. (Differences may be explained by a non-ideal adiabatic boundary condition.) This explanation has not yet been verified with temperature measurements, but it is ancillary to the intent of this paper. In this case, we expect a uniform circumferential distribution, which is predominantly true in both images in Figure 15.

(b) (a) Figure 15: Ratio of ratios [ (B/A)off / (B/A)on ] for the blurred (a) and deblurred (b) cases, displayed in the original Cartesian coordinates.

The ratio of ratios based on the blurred image (Figure 15a) clearly shows artifacts at the leading and trailing edges that corrupt the expected circumferentially-constant distribution. The errors can be quite high, even exceeding 100% error near the trailing edge. Another indicator of blurring is the elongated registration markers that streak in the direction of rotation. In contrast, the deblurred ratio of ratios (Figure 15b) exhibits a very clean distribution that is nearly constant circumferentially. The artifacts at the leading edge have been completely removed. The trailing edge, however, does indicate ringing due to the Gibbs effect. These observations are more clearly seen in a circumferential profile along the total arc length of the painted region at r/R = 0.95, shown in Figure 16. The departure of the blurred solution from the expected straight line is severe over regions of the first 5% and the final 15% of the chord. The deblurred solution, however, has completely ameliorated the leading edge discrepancy and has restored the trailing edge up to the final 5%. The Gibbs ringing in the last 5% of chord is unavoidable in the current analysis due to the high-frequency content of the trailing edge; however, other deconvolution or regularization schemes may be able to solve the distribution more satisfactorily. It should be noted that no spatial filtering has been applied to any of the data sets in this paper. (In this case, spatial filtering is considered a separate endeavor from the regularization process that is considered in the next section.) Spatial filtering would obscure the results of this investigation; furthermore, the unfiltered results are of such high quality that spatial filtering is not needed.



Figure 16: Chordwise profiles of the ratio of ratios [ (B/A) off / (B/A)on ] taken at r/R = 0.95. C. Evaluation of Noise and Regularization The regularization of noise in the deconvolution process is an important parameter to study. As shown in the contrast between Figure 3 and Figure 4, noise regularization can make the difference between acceptable and wholly inadequate results. Based on this understanding of deconvolution, it is therefore surprising that the deblurring results presented in the previous section are of such high quality since there was no regularization applied. This is a particularly striking finding since these images were acquired in a single-shot manner – i.e., there was no image averaging of any kind. Despite this initial success, there remains the question of whether regularization can actually improve upon the results already presented. In order to ascertain the optimum level of regularization, a trade study was performed over a range of noise-to-signal ratios, as shown in Figure 17. The data sets presented here are from identical data reduction schemes, presenting the chordwise intensity distribution of the wind-on Gate B at r/R = 0.95. Higher levels of NSR applied as a regularization parameter in Eq. 17 do indeed reduce the level of high frequency noise in the intensity distribution, and also reduce the Gibbs ringing at the leading and trailing edges. However, this comes at the cost of accuracy. As the NSR parameter is increased beyond small values, the entire intensity distribution loses energy. This behavior is highly problematic for PSP, as it would result in a strong bias error in the measurements. Since the results with no regularization are very acceptable, and the risk of inducing a bias error is great, it is suggested that regularization be avoided for this class of imagers. If reduction of highfrequency noise is still desired, spatial filtering can be judiciously applied in the latter stages of the data reduction process.

Figure 17: Effect of varying the noise-to-signal ratio (NSR) on the deblurring; chordwise intensity profiles of wind on Gate B images at r/R = 0.95. 17 American Institute of Aeronautics and Astronautics


While the interline-transfer camera used for this work yielded excellent results, it is anticipated that some imagers may have higher noise levels. Thus, it is instructive to evaluate the impact of additive noise on the quality of the deblurred solution. The images presented in Figure 18 are the same as those in Figure 11, but with noise added. The variance of the additive noise was 110-4, which corresponds to noise of approximately 100 counts out of 10,000. This level of noise is not substantial enough that it would visibly corrupt the original blurred image; indeed Figure 18(a) appears to be identical to Figure 11(a) upon visual inspection. However, the deblurred results show a striking difference: the noise has been significantly amplified! The image in Figure 18(b) is the result of the same deconvolution procedure (no noise regularization), yet the noise is much more apparent. A comparison of Figure 19 with Figure 12 also shows the same phenomenon. The ratio of ratios in Figure 18(d) has also been corrupted, with the high-frequency noise dominating the distribution. Even though the noise has been amplified substantially, it still may not be prudent to use regularization due to the errors shown in Figure 17. If regularization is used, it must be done carefully. Alternatively, results such as those in Figure 18(b) may be greatly improved through spatial filtering such as an averaging disk filter that adapts to boundary conditions to preserve the edges.

(a)

(b)

(c) (d) Figure 18: Blurred (a) and deblurred (b) views of the tip corner of the wind on Gate B image with noise of var = 110-4 added to the original images shown in Figure 11. Blurred (c) and deblurred (d) images of the ratio of ratios in Cartesian coordinates for the images with added noise.

D. Resolution of Strong Pressure Gradients The current implementation of the deblurring technique assumes a constant value of the luminophore lifetime across the painted surface. Of course, any pressure gradients present will also induce a change in the local luminophore lifetime. It is anticipated that moderate pressure gradients will not induce enough of a change in the lifetime for substantial blurring errors to take place. However, strong pressure gradients such as those produced by a shock may induce blurring errors. This problem could become important if the primary thrust of an investigation is to locate a shock with high spatial resolution. Also, it is anticipated that the impact of a given pressure gradient on the local variation in luminophore lifetime will be particularly severe at lower pressures, due to the nonlinearity of the lifetime calibration curve (see Figure 10).



Figure 19: Chordwise intensity profiles of the noise-added wind-on images, taken at r/R = 0.95. Note the significant increase in noise on the deblurred profile relative to the blurred On B and On A profiles. In order to investigate the impact of strong pressure gradients on the blurring process, a nitrogen jet was mounted on the spinning disk in the rotating frame of reference. The jet was blown across the surface of the PSP as a grazing flow. Due to the presence of the rotary union specifically moutned to the disk for this test, the maximum rotation speed was decreased from 269 Hz to 134 Hz. Also, for this experiment 50 image sets were averaged in order to reduce noise (for reasons to be explained shortly). Otherwise, the experiment was conducted in a similar manner and the deblurring was performed based on the same value of luminophore lifetime corresponding to ambient pressure. Results from this experiment are shown in Figure 20, which is the deblurred ratio-of-ratios in Cartesian coordinates. The exit of the nitrogen jet nozzle is located about midway across the span of the painted region. With the direction of rotation remaining in the counter-clockwise direction, the observed rearward deflection of the jet may be attributed to the Coriolis force since the PSP is in the rotating frame of reference. The capability of the deblurred images to resolve the location of the nitrogen jet is shown in Figure 21 and Figure 22. Each snapshot in Figure 21 corresponds to the same data set, but with different analysis approaches: (a) is the blurred ratio of ratios, (b) is the deblurred case, and (c) is the ratio of the wind-off Gate A divided by the wind-on Gate A. Thus, Figure 21(c) is essentially a intensity-based ratio of two very short (6 s) exposures. This represents an attempt to create a ground truth image for comparison with the other two approaches, since the short wind-on exposure is not nearly as susceptible to image blurring. However, since the exposure time for Figure 21(c) is so short, there is substantially more noise in the image (thus, the reason for averaging 50 images). Also, it should be noted that the images presented in Figure 21 are not calibrated – in particular, the results in image (c) have been scaled to approximately match the other two. Profiles taken at the same location for all three images in Figure 21 are shown in Figure 22, in order to quantitatively illustrate the jet position. A careful examination of Figure 21 reveals that the degree of jet sweep back is reduced for the blurred image (relative to image c), and that image (b) also shows reduced sweep back to a lesser extent. Figure 22 verifies this observation – the off A / on A jet is furthest to the right, while the blurred jet is furthest to the left. Furthermore, the magnitude of the intensity gradient is greatest for the off A / on A jet and is least for the blurred jet. The deblurred jet image falls between the two in terms of location and magnitude of intensity gradient. Under the presence of image blurring, it is expected that intensity profiles will be shifted to the left (the direction of rotation) in Figure 22. This explains why the blurred jet is furthest to the left, and the reasons for the shallow intensity gradient are clear based on the results presented earlier. However, the deblured jet apparently does not entirely correct for the jet location and profile. There still remains an error of about 5 pixels or so, which is likely due to insufficient deblurring with an estimated luminophore lifetime that is too short (locally). These results strongly suggest that a spatially-variant point spread function may be necessary for a complete deblurring process and accurate inference of location and magnitude of a strong pressure gradient. The nitrogen jet employed here is considered a worst-case scenario, but situations involving strong shocks or suction peaks may also require iterative deblurring with a spatially-variant PSF.29,30 19 American Institute of Aeronautics and Astronautics


Figure 20: Deblurred ratio-of-ratios of spinning disk at lower rotational speed with grazing nitrogen jet flow.

(a) (b) (c) Figure 21: Enlargements of the nitrogen jet exit region for the blurred (a), deblurred (b), and “ground truth” (Off A / On A) cases.

Figure 22: Profiles across the nitrogen jet for the three cases shown in Figure 21. The Off A / On A profile may be considered the correct distribution. 20 American Institute of Aeronautics and Astronautics


VI. Conclusion and Recommendations This paper summarizes the current status of image deblurring schemes applied to rotating blades painted with PSP. Image deblurring greatly improves the results by enabling quantitative measurement of pressure information near the leading and trailing edges, where many of the critical features of the pressure distribution are found. Current work illustrates the capabilities of the technique on a rotating disk. The focus of this paper is on improvements to the deblurring scheme and characterizing the sensitivity of the solution to various input parameters. The key change to the algorithm involves a mapping from Cartesian to polar coordinates, which enables application of the deblurring algorithm to images with arbitrarily long blur (high rotational speed and/or long lifetime PSP). The refined image deblurring scheme was evaluated by experiments on a spinning disk, in order to establish the suitability of the technique and sensitivity of the solution to input parameters. The deblurring scheme successfully handled rotational blurs at a rate of up to 269 Hz with a characteristic luminophore lifetime of approximately 10 s. High-frequency ringing in the solution was observed in some cases near edges of the PSP sample, which was attributed to the Gibbs effect. Despite the fact that these are single-shot PSP images with no averaging, the image noise was not a significant problem in the deblurring process. A FFT-based deconvolution scheme without regularization was able to handle the intrinsic noise level of the images. When some noise was added to the images, however, the deblurring scheme greatly amplified this error source. It is suggested that regularization is not necessary in this work, and even should be avoided due to artifacts and bulk-shift bias errors that are introduced. Experiments with a grazing nitrogen jet illustrated the need for a spatially-varying point spread function coupled with an iterative scheme for accurate determination of the magnitude and location of strong pressure gradients. Further work can be done to develop spatially-variant PSF schemes applied to rotating PSP, and other deconvolution algorithms may be evaluated in comparison to the Wiener FFT-based deconvolution used here.

Acknowledgments This work is funded by a NASA Phase I SBIR, monitored by A. Neal Watkins, Luther Jenkins, and Oliver Wong; and by a subaward from the Georiga Tech Vertical Lift Research Center of Excellence. K.J. Disotell acknowledges the financial support of a National Science Foundation Graduate Research Fellowship. The authors wish to thank Bob Guyton of the Air Force Research Laboratory for loaning the photomultiplier tube used to characterize the PSP lifetime decay curves.

References 1.

Bell, J.H., Schairer, E.T., Hand, L.A., and Mehta, R.D., 2001, “Surface pressure measurements using luminescent coatings,” Annual Review of Fluid Mechanics, vol. 33, pp. 155-206, doi: 10.1146/annurev.fluid.33.1.155.

2.

Liu, T., and Sullivan, J.P., 2005, Pressure and Temperature Sensitive Paints, Springer, New York.

3.

Schairer, E.T., 2002, “Optimum thickness of pressure-sensitive paint for unsteady measurements,” AIAA Journal, vol. 40, no. 11, pp. 2312-2318, doi: 10.2514/2.1568.

4.

Gregory, J.W., Asai, K., Kameda, M., Liu, T., and Sullivan J.P., 2008, “A review of pressure-sensitive paint for high-speed and unsteady aerodynamics,” Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol. 222, pp. 249-290, doi: 10.1243/09544100JAERO243.

5.

Sugimoto, T., Kitashima, S., Numata, D., Nagai, H., and Asai, K., 2012, “Characterization of Frequency Response of Pressure-Sensitive Paints,” AIAA-2012-1185, 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Nashville, TN, doi: 10.2514/6.2012-1185.

6.

Gregory, J.W., Sullivan, J.P., Wanis, S., and Komerath, N.M., 2006, “Pressure-sensitive paint as a distributed optical microphone array,” Journal of the Acoustical Society of America, vol. 119, pp. 251-61, doi: 10.1121/1.2140935.

7.

Disotell, K.J. and Gregory, J.W., 2011, “Measurement of Transient Acoustic Fields Using a Single-Shot Pressure-Sensitive Paint System,” Review of Scientific Instruments, vol. 82, no. 7, 075112, (8pp), doi: 10.1063/1.3609866.

8.

Fang, S., Long, S., Disotell, K.J., Gregory, J.W., Semmelmayer, F.C., and Guyton, R.W., 2012, “Comparison of Unsteady Pressure-Sensitive Paint Measurement Techniques,” AIAA Journal, vol. 50, no. 1, pp. 109-122, doi: 10.2514/1.J051167.

9.

Juliano, T.J., Kumar, P., Peng, D., Gregory, J.W., Crafton, J., and Fonov, S., 2011, “Single-shot, lifetime-based pressuresensitive paint for rotating blades,” Measurement Science & Technology, vol. 22, no. 8, 085403 (10pp), doi: 10.1088/09570233/22/8/085403.


10. Juliano, T.J., Disotell, K.J., Gregory, J.W., Crafton, J., and Fonov, S., 2012, “Motion-Deblurred, Fast-Response PressureSensitive Paint on a Rotor in Forward Flight,” Measurement Science & Technology, vol. 23, no. 4, 045303 (11pp), doi: 10.1088/0957-0233/23/4/045303. 11. Wong, O.D., Watkins, A.N., and Ingram, J.L., 2005, “Pressure-Sensitive Paint Measurements on 15% Scale Rotor Blades in Hover,” AIAA 2005-5008, 35th AIAA Fluid Dynamics Conference and Exhibit, American Institute of Aeronautics and Astronautics, doi: 10.2514/6.2005-5008. 12. Wong, O.D., Noonan, K.W., Watkins, A.N., Jenkins, L.N., and Yao, C., 2010, “Non-Intrusive Measurements of a FourBladed Rotor in Hover - A First Look,” American Helicopter Society Specialists’ Conference on Aeromechanics, American Helicopter Society, San Francisco, CA. 13. Wong, O.D., Watkins, A.N., Goodman, K.Z., Crafton, J., Forlines, A., Goss, L., Gregory, J.W., and Juliano, T.J., 2012, “Blade Tip Pressure Measurements Using Pressure Sensitive Paint,” Paper No. 233, American Helicopter Society 68 th Annual Forum, Fort Worth, TX, May 1-3.


14. Watkins, A.N., Leighty, B.D., Lipford, W.E., Wong, O.D., Oglesby, D.M., and Ingram, J.L., 2007, “Development of a Pressure Sensitive Paint System for Measuring Global Surface Pressures on Rotorcraft Blades,” ICIASF Record: Proceedings of the 22nd International Congress on Instrumentation in Aerospace Simulation Facilities, Institute of Electrical and Electronics Engineers, doi: 10.1109/ICIASF.2007.4380888. 15. Watkins, A.N., Leighty, B.D., Lipford, W.K., Wong, O.D., Goodman, K.Z., Crafton, J., Forlines, A., Goss, L.P., Gregory, J.W., and Juliano, T.J., 2012, “Deployment of a Pressure Sensitive Paint System for Measuring Global Surface Pressures on Rotorcraft Blades in Simulated Forward Flight,” AIAA-2012-2756, 28th AIAA Aerodynamic Measurement Technology, Ground Testing, and Flight Testing Conference, New Orleans, LA, June 25-28, 2012, doi: 10.2514/6.2012-2756. 16. Miyamoto, K., Miyazaki, T., and Sakaue, H., 2010, “Development of Motion-Cancelled PSP System and its Application to a Helicopter Blade,” AIAA 2010-4798, 27th AIAA Aerodynamic Measurement Technology and Ground Testing Conference, American Institute of Aeronautics and Astronautics, Chicago, IL, doi: 10.2514/6.2010-4798. 17. Juliano, T.J., Peng, D., Jensen, C., Gregory, J.W., Liu, T., Montefort, J., Palluconi, S., Crafton, J., and Fonov, S., 2011, “PSP Measurements on an Oscillating NACA 0021 Airfoil in Compressible Flow,” AIAA-2011-3728, 41st AIAA Fluid Dynamics Conference, Honolulu, HI, June 27-30, 2011, doi: 10.2514/6.2011-3728. 18. Jensen, C., Gompertz, K., Peng, D., Juliano, T.J., Kumar, P., Gregory, J.W., and Bons, J.P., 2011, “Unsteady Compressible Flow on a NACA 0021 Airfoil,” AIAA-2011-0670, 49th AIAA Aerospace Sciences Meeting, Orlando, FL, January 4-7, 2011, doi: 10.2514/6.2011-670. 19. Jensen, C.D., Gompertz, K.A., Peng, D., Gregory, J.W., and Bons, J.P., 2012, “Measurement Techniques for Shock Movement Capture on a NACA 0012 in Unsteady Compressible Flow,” AIAA-2012-3111, 28th AIAA Aerodynamic Measurement Technology, Ground Testing, and Flight Testing Conference, New Orleans, LA, June 25-28, 2012, doi: 10.2514/6.2012-3111. 20. Disotell, K.J., Juliano, T.J., Peng, D., Gregory, J.W., Crafton, J., and Komerath, N.M., 2012, “Unsteady Pressure-Sensitive Paint Measurements on an Articulated Model Helicopter in Forward Flight,” AIAA-2012-2757, 28th AIAA Aerodynamic Measurement Technology, Ground Testing, and Flight Testing Conference, New Orleans, LA, June 25-28, 2012, doi: 10.2514/6.2012-2757. 21. Yorita, D., Asai, K., Klein, C., Henne, U., and Schaber, S., 2012, “Transition Detection on Rotating Propeller Blades by means of Temperature-Sensitive Paint,” AIAA-2012-1187, 50th AIAA Aerospace Sciences Meeting, Nashville, TN, January 9-12, 2012, doi: 10.2514/6.2012-1187. 22. Klein, C., 2013, “Pressure Measurement on Rotating Propeller Blades by means of the Pressure-Sensitive Paint Lifetime Method,” AIAA-2013-0483, 51st AIAA Aerospace Sciences Meeting, Grapevine, TX, January 7-10, 2013, doi: 10.2514/6.2013-483. 23. Gregory, J.W., Sakaue, H., and Sullivan, J.P., 2002, “Unsteady Pressure Measurements in Turbomachinery Using Porous Pressure Sensitive Paint,” AIAA-2002-0084, 40th AIAA Aerospace Sciences Meeting, Reno, NV, doi: 10.2514/6.2002-84. 24. Gregory, J.W., 2004, “Porous Pressure-Sensitive Paint for Measurement of Unsteady Pressures in Turbomachinery,” AIAA2004-0294, 42nd AIAA Aerospace Sciences Meeting, Reno, NV, doi: 10.2514/6.2004-294. 25. Gregory, J.W., Kumar, P., Peng, D., Fonov, S., Crafton, J.W., and Liu, T., 2009, “Integrated Optical Measurement Techniques for Investigation of Fluid-Structure Interactions,” AIAA-2009-4044, 39th AIAA Fluid Dynamics Conference, San Antonio, TX, doi: 10.2514/6.2009-4044. 26. Hansen, P.C., Nagy, J.G., and O’Leary, D.P., 2006, Deblurring Images: Matrices, Spectra, and Filtering, Society for Industrial and Applied Mathematics, Philadelphia, PA, doi: 10.1137/1.9780898718874.


27. Hansen, P.C., 2010, Discrete Inverse Problems: Insight and Algorithms, Society for Industrial and Applied Mathematics, Philadelphia, PA, doi: 10.1137/1.9780898718836. 28. Gonzalez, R.C. and Woods, R.E., 1992, Digital Image Processing, Addison-Wesley, Reading, MA. 29. Nagy, J.G., Palmer, K., and Perrone, L., 2004, “Iterative methods for image deblurring: a Matlab object-oriented approach,” Numerical Algorithms, Vol. 36, No. 1, pp. 73-93, doi: 10.1023/B:NUMA.0000027762.08431.64. See also http://www.mathcs.emory.edu/~nagy/RestoreTools/ (cited 01-Jan-2013) for a downloadable MATLAB toolbox. 30. Nagy, J.G. and O’Leary, D.P., 1998, “Restoring images degraded by spatially variant blur,” SIAM Journal on Scientific Computing, Vol. 19, No. 4, pp. 1063-1082, doi: 10.1137/S106482759528507X. 31. Vio, R., Nagy, J., and Wamsteker, W., 2005, “Multiple-image deblurring with spatially-variant point spread functions,” Astronomy & Astrophysics, Vol. 434, pp. 795-800, doi: 10.1051/0004-6361:20035754. 32. Joshi, N., Szeliski, R., and Kriegman, D.J., 2008, “PSF estimation using sharp edge prediction,” Computer Vision and Pattern Recognition, 2008. CVPR 2008. IEEE, pp. 1-8, 23-28 June 2008, doi: 10.1109/CVPR.2008.4587834


33. Hirsch, M., Schuler, C.J., Harmeling, S., and Schölkopf, B., 2011, “Fast Removal of Non-uniform Camera Shake,” 2011 IEEE International Conference on Computer Vision (ICCV), pp.463-470, 6-13 Nov. 2011, doi: 10.1109/ICCV.2011.6126276. 34. Joshi, N., Kang, S.B., Zitnick, C.L., and Szeliski, R., 2010, “Image deblurring using inertial measurement sensors,” ACM Transactions on Graphics (TOG), Vol. 29, No. 4, 30, doi: 10.1145/1778765.1778767. 35. Harmeling, S., Hirsch, M., and Schölkopf, B., 2010, “Space-Variant Single-Image Blind Deconvolution for Removing Camera Shake,” Advances in Neural Information Processing Systems 23: Proceedings of the 24th Annual Conference on Neural Information Processing Systems, edited by John D. Lafferty, Christopher K. I. Williams, John Shawe-Taylor, Richard S. Zemel, and Aron Culotta, 6-9 December 2010, Vancouver, British Columbia, Canada, http://books.nips.cc/papers/files/nips23/NIPS2010_0687.pdf. 36. Ribarić, S., Milani, M., and Kalafatić, Z., 2000, “Restoration of images blurred by circular motion,” Proceedings of the First International Workshop on Image and Signal Processing and Analysis, 2000. IWISPA 2000, IEEE, pp.53-60, doi: 10.1109/ISPA.2000.914891. 37. Hong, H. and Zhang, T., 2003, “Fast restoration approach for rotational motion blurred image based on deconvolution along the blurring paths,” Optical Engineering, Vol. 42, No. 12, pp. 3471-3486, doi: 10.1117/1.1621409. 38. Lim, K.B. and Yu, W.M., 2006, “Compact Discrete Polar Coordinates Transform for the Restoration of Rotational Blurred Image,” 12th International Multi-Media Modelling Conference Proceedings, IEEE, doi: 10.1109/MMMC.2006.1651347. 39. Webster, C.B. and Reeves, S.J., 2007, “Radial Deblurring with FFTs,” IEEE International Conference on Image Processing, ICIP 2007, Vol. 1, pp. I-101-I-104, doi: 10.1109/ICIP.2007.4378901. 40. Yuan, Z., Li, J., and Zhu, Z., 2008, “Robust image restoration for rotary motion blur based on frequency analysis,” Optical Engineering, Vol. 47, No. 9, 097004, (15 pp.), doi: 10.1117/1.2981206. 41. Boracchi, G., Foi, A., Katkovnik, V., and Egiazarian, K., 2008, “Deblurring noisy radial-blurred images: spatially adaptive filtering approach,” Image Processing: Algorithms and Systems VI, 68121D, SPIE Proceedings Vol. 6812, edited by Jaakko T. Astola, Karen O. Egiazarian, and Edward R. Dougherty, doi: 10.1117/12.769400. 42. Whyte, O., Sivic, J., Zisserman, A., and Ponce, J., 2012, “Non-uniform Deblurring for Shaken Images,” International Journal of Computer Vision, Vol. 98, No. 2, pp. 168-186, doi: 10.1007/s11263-011-0502-7. 43. Dash, R., Sa, P.K., and Majhi, B., 2011, “Spatial variant motion deblurring of images,” International Computational Vision and Robotics, Vol. 2, No. 1, pp. 80-88, doi: 10.1504/IJCVR.2011.039358.

Journal

of

44. Tigkos, K., 2011, Omni-Directional Image Deblurring, M.S. Thesis IMM-MSC-2011-11, Informatics and Mathematical Modelling, Technical University of Denmark. 45. Egami, Y., Fujii, K., Takagi, T., Matsuda, Y., Yamaguchi, H., and Niimi, T., 2012, “Reduction of Temperature Effect in Pressure-Sensitive Paint Measurements by Model Materials and Coatings,” AIAA-2012-2759, 28th AIAA Aerodynamic Measurement Technology, Ground Testing, and Flight Testing Conference, New Orleans, LA, June 25-28, 2012, doi: 10.2514/6.2012-2759.


Deconvolution-Based Algorithms for Deblurring PSP ...

Deconvolution-Based Algorithms for Deblurring PSP ...

Suggest Documents

PSP PRINT

PSP PRINT

Deep Generative Filter for Motion Deblurring

Deep Video Deblurring

Scale adaptive region selection for deblurring

Patch Mosaic for Fast Motion Deblurring - CiteSeerX

PSP Benefits Management Guide - Ready For Business!

Download-~)) 'Cucusoft PSP Video Converter + DVD to PSP Suite' by ...

PSP -1001 K – PlayStation

4Videosoft PSP Convertisseur - WordPress.com

PSP-VDC: An Adaptation of the PSP that Incorporates Verified ...

Cucusoft PSP Video Converter + DVD to PSP Suite

PSP : GRA Harry Potter I Zakon Feniksa Essentials (PSP)

Porcine Spermadhesin PSP-I/PSP-II Stimulates ... - BioOne

Simultaneous Localization, Mapping and Deblurring

(* Medal Of Honor Cheats For Psp 374

Aktualizacja PSP 22.01.2014

Bladsy 25.psp

AAP/PSP Bulletin Fall2004

4Videosoft PSP Convertisseur - WordPress.com

Adaptive-Neighborhood Image Deblurring - CiteSeerX

psp iso goku.pdf - Google Drive

suikoden psp games.pdf - Google Drive

psp print - UTHM Institutional Repository