On-speckle suppression in IR digital holography - OSA Publishing

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Letter

Vol. 41, No. 22 / November 15 2016 / Optics Letters

On-speckle suppression in IR digital holography VITTORIO BIANCO, PASQUALE MEMMOLO,* MELANIA PATURZO,

AND

PIETRO FERRARO

Institute of Applied Sciences and Intelligent Systems, Italian National Research Council (ISASI-CNR)—Via Campi Flegrei 34, 80078 Pozzuoli (Naples), Italy *Corresponding author: [email protected] Received 4 August 2016; revised 6 October 2016; accepted 9 October 2016; posted 13 October 2016 (Doc. ID 273160); published 7 November 2016

Long-IR wavelength is the best option for capturing digital holograms of large-size, real-world objects. However, the coherent noise level in a long-IR hologram is by far larger than that of a visible wavelength recording, thus resulting in a poor quality of both numerical and optical reconstructions. In this Letter, we show how such coherent noise can be efficiently suppressed by employing an optical scanning multi-look approach, in combination with 3D block matching numerical filtering. Results demonstrate the possibility to obtain near noise-free numerical reconstructions of IR digital holograms of large-size objects, while preserving resolution. We applied this method to the holograms of a rotating statuette. It will be shown that a remarkable contrast enhancement is achievable along with the recovery of object details that otherwise would be lost because of large speckle grains intrinsically due to the source coherence. © 2016 Optical Society of America OCIS codes: (090.1995) Digital holography; (030.6140) Speckle; (110.3080) Infrared imaging; (110.4280) Noise in imaging systems; (100.2980) Image enhancement. http://dx.doi.org/10.1364/OL.41.005226

When a coherent source is used for imaging purposes, the achievable quality is expected to be far worse than that obtainable by incoherent techniques. This is due to the presence of a mixture of multiplicative speckle noise and additive Gaussian noise [1,2]. The rising of speckle patterns can be traced back to the phenomenon of the random walk in the complex plane [3]. Indeed, if the surface roughness is comparable to the wavelength, an object has to be considered as a secondary source of scatterers. Inside one single resolution patch, the detector receives the coherent superposition of signals coming from multiple scattering sources. The intensity of the resultant at each resolution cell presents a rapid fluctuation in the space of the gray level, causing a severe degradation of the resulting image quality. In digital holography (DH), the mixture of speckle and additive noise is hard to model statistically, and it can severely affect the quality of both numerical and optical reconstructions by SLMs [4–7]. Despite DH offering the possibility to store in a 2D matrix of pixel the entire complex wavefront scattered by an object [8], such a source of degradation is 0146-9592/16/225226-04 Journal © 2016 Optical Society of America

one of the main problems in DH for entertainment [9–11], cultural heritage [12], non-destructive testing [13], and homeland security [14,15]. Many efforts have been spent so far to reduce coherent noise in a visible wavelength DH. Bayesian approaches to the denoising problem were demonstrated to be viable ways to reduce noise in DH whenever prior knowledge on the noise statistics can be exploited [16]. In the absence of prior information, non-Bayesian strategies have to be embraced. The most common recording and reconstruction schemes can be basically divided into two classes, namely single-shot and multi-look (ML) techniques. Most of the single-shot techniques work on the single-look (SL) observable and apply digital filters to reduce noise, often at the cost of a deterministic resolution loss [17,18]. In contrast, multi-look DH (MLDH) exploits the acquisition of a number of observables acquired while providing decorrelation between multiple noise patterns [3,19–25]. Many works have been proposed so far where noise decorrelation is introduced in different ways, e.g., by time diversity using a moving diffuser [3,19], multi-wavelength recordings [22], or polarization diversity [20]. A common drawback of all the MLDH methods is the improvement saturation occurring after combining a certain number of looks, so that adding more and more observables to the algorithm does not help the process. Thus, a ML improvement bound exists, which corresponds to the condition of observables with fully uncorrelated noise patterns [14,19–23]. Besides, a hybrid approach has been recently proposed that performs a numerical simulation of a moving diffuser to implement a non-Bayesian ML strategy with one single DH capture [24]. An efficient encoding formula was also developed, which synthesizes a denoised version of the hologram that can be optically propagated for display purposes [25]. In the framework of image processing techniques working on a single image, the BM3D has been demonstrated to yield the best denoising performance [26], also for holographic reconstructions [18,27]. This is based on non-local grouping image fragments chosen according to a certain similarity rule. Each group is 3D-transformed in order to obtain a representation with enhanced sparsity, which is convenient to separate noise components from the useful signal. However, the performance of BM3D turns out to be severely dependent on the signal-to-noise Ratio (SNR), which is typically low in DH reconstructions and provokes incorrect grouping [1].

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holograms. The novel concept introduced by MLDH-BM3D is the enhanced grouping algorithm, which exploits the ML gain to obtain better working conditions to solve the wrong grouping problem [1]. The improvement shown by MLDHBM3D is far beyond the current state of the art in DH at visible wavelengths. The case of IR is more challenging as it corresponds to a different type of speckle pattern. Indeed, the size of the speckle grains in IR holograms is at least one order of magnitude larger than those present in visible recordings. Let λ be the laser wavelength in a lensless DH setup, and let H A N x P x be the hologram aperture in the acquisition plane x; y, where we respectively denoted with N x and P x the number of pixels and the pixel pitch. If z is the distance between the image plane and the hologram plane, the sizes of the speckle grain are proportional to the wavelength as [3,28] sx λz∕N x P x ; s y λz∕N y P y ; (1) Fig. 1. (a) Sketch of the optical scanning setup for multiple holograms recording. In (b) and (c), a comparison between DH at visible and the IR wavelength is shown. (b) Maximum recordable object size, Dz versus z. (c) Size of the speckle grains, Sz versus z.

For this reason, we recently proposed to combine, in the DH framework, the action of MLDH processing to BM3D filtering. The resulting technique, referred to as MLDHBM3D, is demonstrated to provide quasi noise-free reconstructions of holograms recorded at visible wavelengths [1]. Here we analyze the nature of coherent noise in IR digital holography (IRDH), showing that speckle degradation is much more severe than coherent noise for visible wavelengths. Thus, we propose using an optical scanning scheme for recording multiple holograms of a large-size object [see Fig. 1(a)], and adopting the MLDH-BM3D reconstruction algorithm to render a realistic representation of such an object free from coherent artifacts. Notice that, in [1], a rotating diffuser was employed to perform multiple holograms recording with noise diversity while, in the IRDH case, we propose a scanning approach in order to overcome the limitation about the trade-off between the size of the speckle grains and the resolution of the recorded object. The use of object scanning provides noise diversity, and it allows us to set a proper recording distance without sacrificing resolution. In order to reconstruct the entire object, a larger speckle grain has to be accepted, which makes the MLDH preprocessing as key to enabling us to acquire object information. The proposed method shows remarkable results, allowing the full suppression of noise on a large-size statuette reproducing a famous artwork, i.e., the “Bronzo di Riace.” Adopting MLDH is demonstrated to achieve a SNR enhancement and poses better working conditions for the following processing steps. Hence, BM3D can be efficiently employed, i.e., with a low probability of incorrect grouping [1], to remarkably improve the reconstruction quality. We quantify the improvement of the MLDH-BM3D with respect to standard IRDH reconstructions, thus showing the capability of the method to preserve the image resolution while reducing the noise fluctuations, both on flat image areas and signal regions, and achieving a remarkable contrast enhancement. The recently introduced MLDH-BM3D method, mixes the concepts of MLDH processing, NLM, and block matching filtering to obtain a filtering strategy suitable to visible digital

where N y and P y are the number of pixels and their pitch in the y direction. From Eq. (1), it is apparent that, on an equal distance and hologram aperture, the wavelength change when passing from a visible green light (λ 532 nm) to far IR radiation (λ 10.6 μm) provokes an increase of the speckle area of a factor 4 × 102. On the other hand, the choice of a longer laser wavelength allows recording holograms of larger size objects, since the maximum linear dimension of an object that can be recorded without signal undersampling is proportional to the wavelength, too [14]: Dy λd ∕P y ; (2) where d is the object-sensor distance, and we assumed the y dimension of the object to be larger than its size along the x axis. In the case of lensless recordings, z in Eq. (1) turns out to be the distance between the object and the recording device, i.e., it results in z d , and we can substitute Eq. (2) in Eq. (1) to obtain the subjective speckle size S s s y ∕P y Dy ∕N y P y , being the size of the speckle grains in terms of pixels on the recorded hologram. In other words, if we want to capture, by one single exposure, the hologram of an object with the largest linear dimension equal to Dy , we have to accept a speckle grain occupying S S pixels on the hologram. To quantify Eqs. (1) and (2), we report an example referring to the case we afford in this Letter. Figures 1(b) and 1(c), respectively, show the behavior of the recordable size, Dy Dy z, and the corresponding speckle grain size, s y s y z, obtained according to Eqs. (1) and (2) for the IRDH case (yellow line) and a case of visible DH recording where the proposed MLDH-BM3D method was tested (blue line) [1]. The largest linear dimension of the object is DOy ≈ 40 cm, and the parameters of IR recording are λIR 10.6 μm, N y−IR 480, P y−IR 17 μm. In order to avoid the formation of too large speckle grains, we chose a recording distance d 35, 3 cm, assuring the capture of objects with linear size Dy 22 cm. Notice that the effectiveness of the proposed method, in respect to the speckle grain sizes, is mainly related to the MLDH step. More precisely, for a fixed speckle grain, we need to establish the minimum number of looks required to ensure a correct grouping in the BM3D step. In [1,24], a rule has been proposed to select the minimum number of looks to achieve a suitable noise contrast reduction by using the dispersion index metric. Hence, an optical scanning is required to capture information from the entire object. In principle, two recordings would be sufficient at this scope, while more than two vertical

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scans with overlapping areas between adjacent spots can be exploited for the ML purpose [see Fig. 1(a)]. Obviously, when the overall recording time is an issue (e.g., in the case of real-time recording and display), one should choose to maintain the minimum number of spots sufficient to provide an image of the entire object without a further increase of the speckle grain size. According to Eq. (1), the size of the corresponding speckle grain in the recording plane is s_y − IR 458; 3 μm, as reported in Fig. 1(b). This, in turn, results in a subjective speckle size S s−IR ≈ 27 pixel. At the same distance, a visible DH recording (λvis 532nm, P y−vis 6;7μm, N y−vis 1024) would allow us to capture the image of a smaller object (Dy−vis 2; 8 cm), with smaller speckle grain s y−vis 27; 4 μm, i.e., occupying S s−vis ≈ 4 pixel on the hologram. For instance, we can compare the IRDH recording of the bronze statuette to the optical DH acquisition reported in [1], corresponding to the capture of a small puppet with a maximum size DOy 4; 5 cm. Using the set of parameter values (λvis ; P y−vis ; N y−vis ), we find a speckle grain with size s y−vis 43; 82 μm, i.e., 10.5 times smaller than s y−IR , corresponding to a subjective speckle size S s−IR ≈ 6 pixel. Figures 1(b) and 1(c) resume the reported examples. In other words, the use of IRDH is highly required to allow the capture of large-size objects, but the corresponding speckle noise turns out to be much more disturbing for the imaging. Besides, in IRDH the achievable resolution is about 20 times worse than the resolution obtainable in the visible spectrum. Hence, an efficient denoising method is highly demanded in the emerging field of IRDH imaging. The scope of this Letter is to show the performance of MLDH-BM3D in denoising IRDH holograms of large-size objects. To this aim, two experiments have been carried out using the setup in Fig. 1(a). This is a Mach– Zehnder interferometer in reflection configuration. The object is placed on a rotational stage in order to cover the range of angles from θR 0° to θR 360° with the angular step ΔθR 4°. A CO2 laser was adopted with a wavelength λ 10.6 μm. An IR bolometer array was adopted as a sensor, with a pixel pitch P x P y 17 μm. The setup parameters are described in the previous example, providing a speckle grain size of S s−IR ≈ 27 pixel, and the maximum recordable size of Dy 22 cm. Thus, a vertical scanning has to be introduced in order to capture the entire object. In order to acquire different realizations of the noise process, the illumination beam is sent toward a diffuser able to move in two orthogonal directions to provide a linear scanning of the object with diffuse illumination. In a first experiment, the rotating stage was kept static, allowing us to record an arbitrary number of holograms. In particular, we acquired Ly 6 vertical scans (i.e., vertical looks). For each vertical position of the illuminating beam, Lx 6 horizontal looks were captured, corresponding to a total number of looks L Lx Ly 36. In Fig. 2(a), the SLDH reconstruction of the object is shown, where the noise degradation is clearly observable and severely corrupts the image. On the contrary, when the entire sequence of holograms is used as an input of the MLDH-BM3D algorithm [1], a significant improvement is achievable, as shown in Fig. 2(d). The enlarged details extracted from the noisy and denoised reconstructions are reported in Figs. 2(e) and 2(f ), respectively. As a result of noise suppression, the flatness in the background region is improved, while more details of the object become clearly appreciable in the signal region. In general, a remarkable

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Fig. 2. Comparison between noisy and denoised reconstruction of the “Bronzo di Riace.” (a) SLDH. (b) SLDH-BM3D. (c) Optical MLDH. (d) Optical MLDH-BM3D. (e) and (f) Enlarged details extracted from (e) SLDH and (f ) MLDH-BM3D.

improvement in the image contrast is obtained due to the application of the MLDH-BM3D algorithm to IR holograms. This allows overcoming the problems of the large speckle grain and the poor resolution, thus providing a realistic representation of large-size objects. [A photograph of the statuette is reported in Fig. 1(a).] In order to quantify the improvement achieved by MLDH-BM3D, the noise contrast was measured, as described in [1,21,24], for both the noisy and the denoised reconstructions of Fig. 2. The results show an improvement of 91% in the background region and up to 78% in the signal regions. Remarkably, the noise standard deviation is σ MLDH−BM3D 3 × 10−5 , corresponding to a variance improvement of a factor 102. Noteworthy, the SLDH-BM3D reconstruction shows an improvement of 68.9% in the background region, but the incorrect grouping results in poor reconstruction quality in the signal region [Fig. 2(b)]. On the other hand, the sole MLDH does not provide enough improvement [42% in the background region, Fig. 2(c)]. These results are in accordance to what we found in [1]. In a second experiment, the object was put in rotation, and a smaller set of holograms was acquired for each angle. In the lack of enough optical scans of the object, a numerical ML can be fruitfully adopted to reach a similar level of the improvement in terms of SNR. In particular, we used the set of parameters Lx ; Ly 3; 2, corresponding to L 6 looks for each angle. To each hologram of the sequence, random resampling masks were applied to simulate noise diversity, as described in [1,24]. The entire sequence of noisy SLDH reconstructions is reported in Visualization 1, while the corresponding denoised MLDHBM3D images showing the full rotation of the object around its vertical axis are shown in Visualization 2. Some significant frames extracted from Visualization 2 are reported in Fig. 3, as well as some enlarged details extracted from the 3D reconstruction of the statuette, which demonstrate the capability of MLDH-BM3D to work efficiently with a small subset of recordings. The effect of denoising is a clear contrast enhancement, as the signal dynamic on the edges is emphasized. Above all, inside the signal region, the speckle grains are fully crumbled, which allows us to reveal the fine details that were nonvisible in the SLDH. Examples are the object’s chest, abdominals, and beard in Figs. 3 (a) and 3(b); the shine of light on the arm muscles in Fig. 3(c); and the hair in Fig. 3(d). Remarkably, in the detail of Fig. 3(c), the object’s fingers get

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Acknowledgment. This work was supported Databenc, project SNECS-PON03PE_00163_1.

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REFERENCES

Fig. 3. (Visualization 1 and Visualization 2.) IR holograms of the object rotated by 360° without and with MLDH-BM3D processing with the aim to compare the noisy and denoised images for each angle. (a) θR 80°. (b) θR 120°. (c) θR 200°. (d) θR 260°.

resolvable as an effect of denoising. In the case of numerical MLDH-BM3D, we measured a noise contrast gain up to 80%, with a residual noise standard deviation σ MLDH−BM3D 1.1 × 10−4 . These results clearly show the effectiveness of the MLDH-BM3D approach in reconstructing far-IR holograms providing a faithful rendering of large-size physical objects, despite the degradation due to the large size of the speckle grains. In conclusion, in this Letter, we tackled the problem of coherent noise in IRDH acquisitions, where the speckle grain is typically larger in respect to visible DH. Moreover, the longer wavelength results in poorer resolution, making the noise problem much more troubling. On the other hand, the use of the IR range allows capturing holograms of large-size objects, which is highly demanded [14,15]. A trade-off between the maximum achievable object size and the corresponding speckle grain has been discussed in this Letter. Instead of limiting such a distance at the scope of limiting the size of the speckle grains, a more elegant approach is to choose it appropriately to illuminate the entire object by beam scanning, and then to apply a proper denoising strategy to get rid of the speckles. We performed IRDH of a statuette in order to show the efficiency of the MLDH-BM3D algorithm in providing quasi noise-free reconstructions, with quality comparable to low coherence techniques. A contrast enhancement is gained. Remarkably, noise reduction does not produce a smoothing in the signal region. Instead, the resolution loss due to coherent noise is prevented, thus allowing appreciating finer object details and clearly showing the possibility to get rid of the coherent artifacts in IRDH, which was a pivotal goal to the delivery of holographic products to the market of entertainment.

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