Large object investigation by digital holography with

Large object investigation by digital holography with effective spectrum multiplexing under single-exposure approach Ning Liu, Yingying Zhang, and Jun Xie Citation: Applied Physics Letters 105, 151901 (2014); doi: 10.1063/1.4898133 View online: http://dx.doi.org/10.1063/1.4898133 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/105/15?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Frequency Shifted Digital Holography for the Measurement of Vibration with Very Small Amplitudes AIP Conf. Proc. 1253, 415 (2010); 10.1063/1.3455485 Extended depth of focus in a particle field measurement using a single-shot digital hologram Appl. Phys. Lett. 95, 201103 (2009); 10.1063/1.3263141 Spread Space Spread Spectrum Technique for Secure Multiplexing AIP Conf. Proc. 949, 138 (2007); 10.1063/1.2812289 Recent progress in bidirectional interrogation techniques for enhancing multiplexing capability of fiber optic white light interferometric sensors Rev. Sci. Instrum. 74, 4893 (2003); 10.1063/1.1614434 Space–time digital holography: A three-dimensional microscopic imaging scheme with an arbitrary degree of spatial coherence Appl. Phys. Lett. 75, 2017 (1999); 10.1063/1.124901

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APPLIED PHYSICS LETTERS 105, 151901 (2014)

Large object investigation by digital holography with effective spectrum multiplexing under single-exposure approach Ning Liu,a) Yingying Zhang, and Jun Xie College of Physics and Electronics, Nanjing XiaoZhuang University, Nanjing, Jiangsu Province 211171, China

(Received 2 September 2014; accepted 2 October 2014; published online 13 October 2014) We present a method to investigate large object by digital holography with effective spectrum multiplexing under single-exposure approach. This method splits the original reference beam and redirects one of its branches as a second object beam. Through the modified Mach-Zehnder interferometer, the two object beams can illuminate different parts of the large object and create a spectrum multiplexed hologram onto the focal plane array of the charge-coupled device/ complementary metal oxide semiconductor camera. After correct spectrum extraction and image reconstruction, the large object can be fully observed within only one single snap-shot. The flexibility and great performance make our method a very attractive and promising technique for C 2014 AIP Publishing LLC. large object investigation under common 632.8 nm illumination. V [http://dx.doi.org/10.1063/1.4898133]

In modern optics, digital holography (DH) has been applied in many fields, such as microscopy,1,2 3D imaging,3 metrology,4 display technology,5 and so on. It has the great ability to reconstruct not only the intensity but also the phase information of a transparent or reflective object. This gives us great flexibility to study the tiny structure of an object. Progress has been achieved in recent years.6,7 However, people are still encountering an inevitable problem when conducting DH, which is how to sample a large object due to the limited pixel size of the charge-coupled device (CCD)/ complementary metal oxide semiconductor camera (CMOS). In some applications, especially in the lensless digital holography, when the size of an object is much bigger than the size of the focal plane array (FPA) of CCD/CMOS camera, the total information of the object cannot be fully recorded by the camera. A lot of work have been done in recent years to solve this problem, and they can be categorized into three groups: multiple exposures methods,8–11 single exposure method,12 and long wave spectrum method.13,14 The multiple exposures methods record a series of sub-holograms on different frames of a CCD in sequence, and reconstructed image covering a much larger area can be obtained by digital synthesis technology. However, this approach cannot be applied to dynamic processes. Although a zoom lens can be used to expand the sampled area of a dynamic process, the resolution of the reconstructed image would be reduced due to the fixed pixel number and the size of the CCD/CMOS. The long wave spectrum method is mostly focused by an excellent Italian research group in recent years.13,14 They use the 10.6 lm CO2 laser as the light source in order to record large objects due to the advantage of the long wavelength. This approach can achieve great effort of recording very large objects such as human sized objects. But due to the long wave infrared spectrum, the difficulty of the experimental setup is way much bigger than the He-Ne laser. a)

Author to whom correspondence should be addressed. Electronic mail: [email protected]

0003-6951/2014/105(15)/151901/3/$30.00

Meanwhile, the resolution of the recorded hologram is much smaller than the one captured by the visible light CCD/ CMOS because of the low resolution of infrared cameras. Recently, a new single exposure method has been published using two laser sources to record large objects.12 This method uses a 632.8 nm laser and a 532 nm laser to illuminate the object. With complicated setup of the optical path, one object can be separated into four pieces and four incoherent sub-holograms can be recorded and overlapped in one single frame of the CCD. After stitching and fusion technology, a large sampled area of the object can be finally obtained by combining the four pieces together. This method is really mind-opening for the large object investigation, but somehow it includes too many optical components setup and laser sources. More than 20 optical components are involved in the experimental setup, which makes the experiment inconvenient to conduct. Although the method is great, it is hard for repetition. In this letter, we present a large object investigation method based on effective spectrum multiplexing. This method is very simple in experimental setup with only one 632.8 nm laser source and very few optical components. It works quite well in the single-exposure approach, which makes it very convenient. With this method, we can greatly improve the ability of observing large objects under 632.8 nm He-Ne laser in the lensless application. The test sample is a miniature monument of 2010 U.S. census shown in Fig. 1. We choose one of the characters as the observing object. The chosen character has been spot out with brown rectangle. The dimension of this character is 1 cm  1.2 cm. The dimension of the FPA of CMOS camera is 1280  1024 with the pixel distance of 5.2 lm. According to mathematical calculation, in lensless digital holographic setup, we cannot fully observe such big object with the camera. Microobjective lens could be used to fulfill this situation, but it is not the concern of this letter. The experimental setup of this method is shown in Fig. 2.

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C 2014 AIP Publishing LLC V

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Appl. Phys. Lett. 105, 151901 (2014)

FIG. 1. Demonstration of the test sample.

As we can see, this experiment is quite simple for repetition. The whole optical setup is based on the Mach-Zehnder interferometer, and slight modification has been added to the optical path to accomplish the large object investigation. The main idea of this method is to split the laser and illuminate the different parts of the large object. With each beam carries the different information of the object, a mixed hologram containing different parts of the object will be generated. We can demodulate all the parts of the object from the mixed hologram, and the full object can then be acquired. The modification of the optical path is described as follows: in order to create a second illumination, we add a beam splitter No. 2 (BS2) in the original reference wave path and direct it towards the BS3. Usually in the Mach-Zehnder interferometer setup, the mirror in the location of BS3 is a reflective mirror. We change it to a beam splitter so that the light directed from BS2 can go through it. Mirror No. 2 (M2) and No. 3 (M3) are two reflective mirrors; they redirect the light coming through BS3 into the direction which the original object wave goes. Thanks to these two mirrors, the illumination direction of the red beam can be easily adjusted in a slight

FIG. 2. The optical setup of this experiment.

angular scale to illuminate the other part of the object which the original object wave cannot. These two object beams (red beam and black beam) will be direct into the FPA of the CCD/CMOS in nearly the same direction but with a small angle. The intensity distribution of the mixed hologram can be written and modified as15 Iðx; yÞ ¼ jO1 þ O2 þ Rj2 :

(1)

Equation (1) can be expanded as Iðx; yÞ ¼ jO1 j2 þ jO2 j2 þ jRj2 þ O1 R þ O1 R þ O2 R þ O2 R þ O1 O2 þ O1 O2 ;

(2)

where Rðx; yÞ represents the reference wave and O1 ðx; yÞ and O2 ðx; yÞ represent the original object wave and the second object wave, respectively, and * denotes the complex conjugate. According to Eq. (2), if we perform the Fourier transform onto the mixed hologram,6 jO1 j2 þ jO2 j2 þ jRj2 will be the dc component, and three kinds of object spectrum of (O1 R ; O1 R), (O2 R ; O2 R), and (O1 O2 ; O1 O2 ) will be shown in the frequency domain. Unlike the method raised in Ref. 12, here we only use a single laser to accomplish the large object investigation. That is to say, when generating the mixed hologram, the polarization direction of O1 , O2 , and R has to be suitably adjusted. Otherwise, the features of the interference fringes of (O1 , R) and (O2 , R) will be nearly the same and hard to distinguish in the frequency domain. Meanwhile, because we use a single laser, O1 and O2 will interfere at the same time, and this will cause frequency aliasing problem on (O1 , R) and (O2 , R). So, as shown in Fig. 2, a polarizer is added in the optical path of O1 to adjust the polarization state. In this case, the interference fringes of (O1 , R) and (O2 , R) will be in the different tilt directions with different angles. During the experiment, the polarizer in Fig. 2 sets the angle as 45 so that the spectrum of the interference of (O1 , O2 ) will be very close to the dc component, and the frequency aliasing will vanish. Once the optical setup is correct, we can easily acquire all the frequency spectrums of the different parts of the object with only one single snap-shot. We can spot out these spectrums and conduct the inverse Fourier transform to reconstruct the different object

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FIG. 3. Spectrum multiplexing illustration of the mixed hologram and the different object parts reconstruction. (a) Mixed hologram. The yellow rectangle indicates the three kinds of interference fringes mixed together. The red, green, and blue rectangles spot out the different interference fringes of (O1 , R), (O2 , R), and (O1 , O2 ), respectively. (b) Spectrum separation according to correct optical path setup. The red, green, and blue rectangles spot out all the þ1 order of Eq. (2). (c) and (d) The image reconstruction of (O1 , R) and (O2 , R), respectively.

parts.6 The whole object can then be synthesized by the reconstructed images. The above discussion is illustrated in Fig. 3. Fig. 3 clearly shows the spectrum multiplexing and reconstructing process under single-exposure approach. The full object information can then be synthesized by Figs. 3(c) and 3(d). The result is shown in Fig. 4 as follows. It can be seen from Fig. 4, after the whole process of this experiment, the object much larger than the FPA has been fully acquired. Although we cannot fully investigate the whole character with the traditional digital holography under single 632.8 nm He-Ne laser, with the method proposed in this letter, this task becomes achievable without any micro-objective lens participate in the optical path. In conclusion, we have proposed a method to investigate large objects by digital holography. This method uses the spectrum multiplexing under single-exposure approach. The advantage of this method is threefold. First, this method can be achieved with very few optical components. This makes the method very easy for repetition. Second, the proposed

Appl. Phys. Lett. 105, 151901 (2014)

FIG. 4. Final result of the large object investigation with spectrum multiplexing.

method is much simpler, stable, and controllable than the one raised in Ref. 12. Finally, this method needs no long wave infrared laser to fulfill this task13,14 and can investigate objects much bigger than the FPA under 632.8 nm illumination. We are sure that this method will give help in large object investigation with common He-Ne laser in the future. 1

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