Coded Aperture Incoherent Digital Holography - OSA Publishing

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2016 Imaging and Applied Optics Congress (3D, AO, AIO, COSI, DH, IS, LACSEA, MATH) © OSA 2016

Coded Aperture Incoherent Digital Holography A.Vijayakumar,1 Yuval Kashter,2 Roy Kelner,3 and Joseph Rosen4 Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 8410501, Israel 1 [email protected], [email protected], [email protected], [email protected]

Abstract: A new incoherent digital holography concept using a coded aperture is proposed. Holograms of an object and a point object are recorded under identical conditions. The image is reconstructed by correlating the two holograms. OCIS codes: (100.6640) Superresolution; (090.1995) Digital holography; (110.0110) Imaging Systems, (110.0180) Microscopy; (090.1760) Computer holography; (050.5080) Phase shift; (050.0050) Diffraction and gratings; (060.4785) Optical security and encryption.

1. Introduction Imaging systems can be broadly classified into laser-based coherent systems and incoherent systems. Incoherent imaging systems may offer certain advantages over coherent imaging systems, including low cost light sources and speckle-free imaging [1,2]. This applies to digital holography systems as well. Even though the field of holography gained rapid development due to the invention of the laser, digital holography systems using incoherent light sources have recently attracted attention due to various advantages they possess. One such system is the selfinformative-reference holography system dubbed Fresnel incoherent correlation holography (FINCH), which was invented in 2007 [3,4]. In FINCH, the width of the optical transfer function (OTF) is twice of that of a conventional coherent imaging system of similar numerical aperture (NA), and has a uniform response to all the frequencies of the OTF [5,6]. As a consequence, the resolving power of FINCH is around 2 times and 1.5 times that of equivalent coherent and incoherent imaging systems, respectively. According to a previous study [6], FINCH also exhibits a large depth of focus in the reconstructed images, resulting in a low axial resolution. Recently, FINCH configurations that can suppress out-of-focus information and achieve enhanced axial resolution were proposed and demonstrated, using a single- or multiple-scanning phase pinholes [7,8]. However, the above configurations require two spatial light modulators (SLMs), whereas only one is needed in a regular FINCH system. In this study, we propose a new incoherent self-informative-reference digital holography system dubbed coded aperture correlation holography (COACH). In COACH, a coded random-like phase mask (CPM) is employed to constrict the hologram reconstruction depth of focus to a relatively narrow axial region. In addition, the CPM encrypts the hologram, in the sense that in order to reconstruct the image of the recorded object, the CPM values related knowledge is required. Thus, COACH is a method of three-dimensional (3D) holographic encryption for incoherent illuminated, or self-luminous, objects. When compared with FINCH, the proposed method offers superior axial resolution. 2. Methodology In the proposed system, at least two holograms are recorded under identical conditions, with the same CPM: one hologram contains the information of the object under observation; another is recorded using a point source, in order to acquire the point spread function (PSF) for reconstruction. The image of the object at a certain plane is reconstructed by correlating the complex object hologram with the complex PSF recorded at the same plane, in a similar fashion to [9]. Due to the randomness-like nature of the CPM, even a slight deviation in the axial distance of the pinhole, or of the object, distorts the reconstructed image at the plane of interest significantly, resulting in a rapid fall of the reconstructed image intensity. Therefore, in order to image a thick object using COACH, a library of PSF holograms should be coached by recording them at various planes enabling reconstruction of the object hologram at these planes. The optical configuration of COACH is shown in Fig. 1. Light from an incoherent light source is focused by the lens L1 onto an object in a critical illumination configuration [10]. The light source is spatially incoherent and so the light emitted by each object point is assumed to be coherent only with itself. Therefore, every two beams originating from the same object point are coherently interfered, encoding the information of the intensity and the location of the particular object point. The light diffracted by the object point is collected and collimated by the lens L2. The collimated light is polarized by the polarizer P1 to an orientation of 45o with respect to the active axis of the SLM. Instead of a quadratic phase mask, as in FINCH, a random-like phase profile, constituting the CPM, is displayed on the SLM. The CPM is calculated using the Gerchberg-Saxton (G-S) algorithm to obtain uniform intensity in the spectrum domain [11]. As the polarization of the collimated light is oriented at 45 o with respect to the active axis of

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the SLM, only about half the intensity of the incident light is modulated by the CPM, while the remaining half traverses without any modulation. A second polarizer P2, with an orientation of 45o with respect to the active axis of the SLM, is mounted after the SLM to allow the propagation of only identically oriented components of the modulated and unmodulated waves to create interference between them at the sensor plane. The above polarization multiplexing scheme creates a compact, single channel optical configuration [12]. A phase shifting procedure, similar to [3], is used, where three holograms corresponding to three CPM phase shifts of θ = 0o, 120o, and 240o are recorded and are superposed to cancel the twin image and the zeroth order terms. The complex hologram for an object is the object hologram Hobject. The object is then replaced by a pinhole at the exact location and a hologram HPSF is recorded with identical conditions. The HPSF and Hobject, when correlated, yield the reconstructed image at the plane of the pinhole.

Fig.1. COACH configuration for recording object and PSF holograms.

3. Experimental results The principle of COACH is experimentally demonstrated using the digital holographic setup shown in Fig. 2. A light emitting diode (LED) is used for illuminating the object. A biconvex lens L1 was mounted to critically illuminate the object [10]. United States Air Force (USAF) chart was used as the object and elements 2 (4.49 lp/mm) and 3 (5.04 lp/mm) of group 2 of USAF chart were illuminated. The light diffracted by the object is collimated by a biconvex lens L2 with a focal length of 20 cm, placed in a distance of z0 = 20 cm away from the object. From the lens L2, the light propagates through the polarizer P1, oriented at an angle of 45o with respect to the active axis of SLM. A CPM, calculated using G-S algorithm [11], was displayed on the SLM using 1080 × 1080 pixels. About half of intensity of the light is modulated by the CPM while the remaining propagates as an unaffected beam. As per the phase-shifting method, three CPMs corresponding to θ = 0o, 120o and 240o were displayed in the SLM for eliminating the twin image and the zeroth order terms.

Fig. 2. Experimental set up of COACH.

The distance between L2 and SLM was 11 cm. The distance between the SLM and the beam splitter was 5 cm. A polarizer P2 oriented at 45o with respect to the SLM’s active axis was used to pass components of the modulated and unmodulated light (from SLM) with same orientation, to enable interference between them in the sensor plane (Hamamatsu ORCA-Flash4.0 V2 Digital CMOS, 2048 × 2048 pixels, 6.5 μm pixel pitch, monochrome). The distance between the SLM and the CMOS sensor was zh = 15 cm. The object holograms Hobject for the three phase

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shift values were recorded and superposed [3]. Similarly, PSF holograms HPSF with three phase shift values were recorded by replacing the USAF with a pinhole (10 µm). The image was reconstructed by correlating Hobject with HPSF. The experiment was carried out by recording Hobject by varying the location of the USAF charts from 0 cm to 3 cm (z0 = 20 – 23 cm) in steps of 1 cm with respect to the location of the point object followed by the recording of HPSF at f0 = 20 cm. The image was reconstructed by correlating the PSF hologram with the object holograms. Image of the CPM displayed on the SLM and images of HPSF and Hobject, recorded by the image sensor before applying the phase shift, are shown in Figs. 3 (a), (b) and (c) respectively. The result obtained with COACH was compared with regular imaging, as well as with FINCH, in a configuration similar to [3], as shown in Fig. 3(d). It can be noted that FINCH demonstrates a relatively low axial resolution, as expected from the previous analysis [6], and as mitigated by a rather low amount of defocusing. COACH, on the other hand, shows a higher axial resolution, when compared to FINCH, and somewhat similar performance, when compared to regular imaging.

Fig. 3. Images of (a) the CPM, displayed on the SLM, (b) HPSF and (c) Hobject, as recorded by the image sensor, and (d) experimental comparison results of regular imaging and reconstruction of the FINCH and COACH holograms.

4. Conclusion We have proposed and demonstrated COACH, a new digital incoherent holographic system that possesses higher axial resolving power compared to FINCH. COACH is actually a generalized incoherent digital hologram recorder, in the sense that FINCH [3, 4] may be considered a special case of COACH, in which the CPM is a quadratic phase function, rather than the arbitrary CPM used for COACH. This special case can violate the Lagrange invariant [6], but COACH, in the presented case, does not and therefore does not possess higher lateral resolution as FINCH. This work was supported by the Israel Ministry of Science, Technology and Space and by the Israel Science Foundation (ISF) (grant no. 439/12). 5. References [1] B. M. Oliver, “Sparkling spots and random diffraction,” Proc. IEEE (Lett.) 51, 220-221 (1963). [2] P. S. Considine, “Effects of Coherence on Imaging Systems,” J. Opt. Soc. Am. 56, 1001-1009 (1966). [3] J. Rosen, and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. 32, 912-914 (2007). [4] J. Rosen, and G. Brooker, “Fluorescence incoherent color holography,” Opt. Express 15, 2244-2250 (2007). [5] J. Rosen, N. Siegel, and G. Brooker, “Theoretical and experimental demonstration of resolution beyond the Rayleigh limit by FINCH fluorescence microscopic imaging,” Opt. Express 19, 26249-26268 (2011). [6] J. Rosen and R. Kelner, “Modified Lagrange invariants and their role in determining transverse and axial imaging resolutions of selfinterference incoherent holographic systems,” Opt. Express 22, 29048-29066 (2014). [7] R. Kelner, B. Katz, and J. Rosen, “Optical sectioning using a digital Fresnel incoherent-holography-based confocal imaging system,” Optica 1, 70-74 (2014). [8] R. Kelner and J. Rosen, “Parallel-mode scanning optical sectioning using digital Fresnel holography with three wave interference phaseshifting,” Opt. Express 24, 2200-2214 (2016). [9] M. K. Kim, “Adaptive optics by incoherent digital holography,” Opt. Lett. 37, 2694–2696 (2012). [10] D. J. Goldstein, Understanding the light microscope: A computer aided introduction, 1st ed. (Academic press, 1999) pp. 9-12. [11] R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 227–246 (1972). [12] G. Brooker, N. Siegel, V. Wang, and J. Rosen, “Optimal resolution in Fresnel incoherent correlation holographic fluorescence microscopy,” Opt. Express, 19, 5047-5062 (2011).