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Abstract
Complete control of a beam pattern requires not only projecting a two-dimensional (2D) pattern but also focusing on a three-dimensional (3D) point cloud, which is typically achieved utilizing holography under the framework of diffraction. We previously reported direct focusing from on-chip size surface-emitting lasers that utilize a holographically modulated photonic crystal cavity based on 3D holography. However, this demonstration was of the simplest 3D hologram with a single point and single focal length, and the more typical 3D hologram with multiple points and multiple focal lengths has not yet been examined. Toward direct generation of a 3D hologram from the on-chip size surface-emitting laser, we here examined a simple 3D hologram featuring two different focal lengths with a single off-axis point in each to reveal the fundamental physics. Two types of holography, one based on superimposition and the other on random tiling, successfully demonstrated the desired focusing profiles. However, both types caused a spot noise beam in the far field plane due to interference between focusing beams with different focal lengths, especially in the case of the superimposing method. We also found that the 3D hologram based on the superimposing method consisted of higher order beams including the original hologram due to the manner of the holography. Secondly, we demonstrated a typical 3D hologram with multiple points and focal lengths and successfully showed the desired focusing profiles by both methods. We believe our findings will bring innovation to mobile optical systems and pave the way to developing compact optical systems in areas such as material processing, micro fluidics, optical tweezers, and endoscopy.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Semiconductor lasers are indispensable for sustaining modern society thanks to their compactness, high efficiency, and high reliability [1]. They are mainly categorized into two types: edge-emitting lasers, which typically show an asymmetric elliptic beam pattern, and surface-emitting lasers, which show a circular beam pattern. Further evolution has been achieved by incorporating two-dimensional (2D) photonic crystals into the lasing cavity of surface-emitting lasers. The photonic-crystal surface-emitting lasers (PCSELs) proposed by Noda’s group successfully demonstrated large-area coherent lasing that gave rise to extremely narrow spot beams [2–9]. They later developed the Modulated-PCSEL (M-PCSEL), in which positional and areal shifts are introduced into the PC cavity [7–9]. Based on the PCSEL technologies, we incorporated the concept of holographic modulation into the 2D PC cavity. Holographic modulation is achieved by the positional and areal shifts of the holes in the holography, such as detour phase hologram or binary hologram [10–12], which has been in use as far back as the 1960s. We incorporated the holographic modulation into the 2D PC cavity and proposed integrable phase modulating surface-emitting lasers (iPMSELs) that directly project the 2D beam pattern from the on-chip size [13–18]. After proving the concept [13], we successfully demonstrated versatile 2D beam patterns including asymmetric ±1st order beam [14], removal of 0th order beam [15] with the aid of the concept of M-PCSEL, which utilizes the M-point band edge), visible wavelength [16], and structured illumination for 3D measurement [17]. Note that holographic modulation of grating coupler had also successfully demonstrated by such as the off-plane computer-generated waveguide hologram (OP-CGWH) [19], it works in non-resonant condition and causing the localization of intensity profile in the grating coupler. Meanwhile, as the iPMSEL utilized the resonant condition based on the platform of the PCSEL in which the 2D coupling of the in-plane lightwaves [20,21] causes a 2D standing wave in entire region of 2D PC, so the localization of intensity profile is suppressed even in a large lasing cavity, thus leading to high quality of beam pattern.
We previously extended our hologram design from the 2D regime to 3D based on the Fresnel diffraction theory [22] and successfully demonstrated direct focusing from the iPMSEL [23], which emits an on-axis single spot and single focal length of the focusing beam, i.e., the simplest 3D hologram. However, the more common 3D hologram with multiple points and focal lengths has not yet been examined. (Note that we recently demonstrated the 1D focusing beam from similar lasing cavity using 3D hologram that enables low noise fringe pattern for the 3D measurement system. [24].) Although the 3D hologram technique has long been established [12], direct emission of a 3D hologram from the on-chip size of a surface-emitting laser is challenging because it restricts the implementation of the optical system due to necessitating the use of additions such as a spatial filter to cut out the noise beam. Toward a more robust design, it is important to establish a basic understanding of the physics. We therefore started from a simple 3D hologram featuring two different focal lengths with a single off-axis point in each to reveal the fundamental physics. Since a 3D hologram is essentially multiplexing of multiple 3D holograms with different focal lengths [25], we first examined the commonly utilized superimposing method. While it successfully showed the desired focusing profiles, strong spot noise beams were observed in the far field planes. In addition, we found that the 3D hologram based on the superimposing method consisted of higher order beams including the original hologram due to the manner of the holography. These noise beam patterns in the far field plane may cause overexposure at unexpected positions, especially when used in narrow regions such as the in-vivo environment. We therefore also examined the approach based on random tiling of the 3D holograms with a different single focal length [26–28]. This method successfully showed the desired focusing profiles and was also able to suppress the noise beams. Second, we examined a more complicated 3D hologram with multiple points and focal lengths for demonstration of a typical 3D hologram. Both holographic methods successfully showed the desired focusing profiles and the noise beam patterns were not noticeable in the far field plane because there were too many pattern points to recognize a particular interference.
In this paper, we report the basic characteristics of the 3D hologram with multiple points and focal lengths from the holographically modulated 2D PC cavity. We first briefly describe the device structure and then move on to the details of the two types of 3D holography (superimposing and random tiling). Next, we describe the measurement setup and discuss the experimental results including lasing characteristics, focusing profiles, and far field patterns. Finally, we show a demonstration of the typical 3D hologram with multiple points and multiple focal lengths.
2. Device structure
The device structure is similar to that in our previous paper [23] except for the hologram design. Figure 1(a) shows the schematics of the device structure. First, the n-AlGaAs cladding layer, i-InGaAs/AlGaAs active layer, and i-GaAs layer are grown on n-GaAs substrates by metalorganic chemical vapor deposition (MOCVD). Next, the holographically modulated PC structure, where the hole is rotated around the periodic lattice point of the 2D PC in accordance with the phase distribution (as shown in Fig. 2(b)), is fabricated on the GaAs layer by EB lithography and dry etching. The lattice constant a, filling factor (areal ratio of the hole against the unit cell), and radius of the circle where the center of the gravity of the hole is rotating r are 202 nm, 28%, and 0.08 a, respectively. This layer acts simultaneously as a lasing cavity and a holographic modulator, so we call it the phase modulating layer hereafter. After the formation of the phase modulating layer, the p-AlGaAs cladding layer and p-contacting layer are grown successively using MOCVD, and the p and n electrodes are then formed using ordinary lithography. The output beam is the basic 3D point cloud hologram consisting of two different focal lengths with a single off-axis point in each. A cross-section in the X-axis is shown in Fig. 1(c). The focal lengths are f1 = 1 mm and f2 = 2 mm. In-plane components of the wavevector on the focal length f1 are k1 = (0.095,0) µm-1, which roughly corresponds to 5° in the X-axis at the far field plane, while those in focal length f2 are k2 = (-0.095,0) µm-1.
Fig. 1. Structure of iPMSEL: (a) perspective view, (b) manner of shifting holes in the phase modulating layer, and (c) cross-section in X-axis.
3. Design of 3D hologram
We designed the hologram of the 3D point cloud as follows. According to the Fresnel diffraction integral [22], the diffraction field is given by the Fourier transform of the product of the complex object field and a quadratic exponential, as
The next challenge is how to superimpose the holograms of different focal lengths. The conventional approach is to simply add the complex amplitude [25]. Considering the multiple points of focusing phase ϕi (i = 1, 2, 3, …, N) at different focal lengths fi, the addition of the complex amplitude is given by adding the complex exponential, as
so that the superimposing phase is simply given asThe other approach is random tiling [26–28]. First, all pixels in the object field are assigned a random number and then classified into N part of the region according to the number. Next, the ith focusing phase ϕi is tiled on the position of the ith region defined by the random number. All phases are tiled in the above manner. Because each of the phases is spatially distributed randomly, the diffraction in a particular direction is suppressed and the focusing behavior is kept at each focal length.
Finally, the phase of the shift vector that diffracts in-plane lightwaves of the M-point band edge within the light line is added [15]. It is described as ϕShift(r) = (π/a)(Ma + Na), where M and N are integers respectively corresponding to the number of the lattice point of the hole in the X- and Y-axes. For intuitive understanding, the above calculation process is summarized in Fig. 2 and the beam patterns of each step are depicted in Fig. 3. As shown in Fig. 3(a)(b), a hologram of a multi-point pattern and a hologram of a single focal length are formed, and then a multi-point focusing hologram is formed by adding the two, as shown in (c). Figure 3(d) shows how the hologram for each focal length is calculated for a hologram having multiple focal lengths. The 3D hologram with multiple points and multiple focal lengths is calculated by superimposing or random tiling, as shown in Fig. 3(e), where the phase of the superimposing method Φ is shown in (f) and that of the random tiling method ϕR in the case of two phases is depicted in (g). Finally, the phase of shift vector ϕshift(r) is added in the case of utilizing the M-point band edge. The 3D hologram utilized in this work is obtained by the above procedure. The details of the phase distributions are discussed in S2.
Fig. 3. Schematic of multiple points and multiple focal lengths of point cloud hologram. (a) Multi-point hologram, (b) focusing hologram, (c) hologram of multiple points at a single focal length, (d) two holograms in different focal lengths, (e) 3D hologram, (f) phase of the superimposing method, and (g) phase of the random tiling method.
4. Measurement setup
We used the same basic setup for measuring the lasing characteristics as that in our previous work [23]. Here, we briefly describe the setup including the light-output characteristics (L-I curve), spectrum, FFP, and focusing profile. The laser chip was operated by an LD driver (ILX lightwave, LDP-3830) with a Peltier controller (Daitron, DPC-100). The pulse width, duty, and operation temperature were 50 ns, 1%, and 25 °C, respectively. The light output power was measured by a photodiode with a neutral density filter (Ophir, PD300-3W-v1) placed in front of the laser chip. The spectrum was measured by an optical spectrum analyzer (Yokogawa, AQ6373) through a single-mode fiber (Optron Science, SM98PKSP). The focusing beam profile was acquired by the setup for the near field pattern (NFP), as shown in Fig. 4. The output beam from the laser chip was collimated by an objective lens and measured by a CCD camera (Hamamatsu, ORCA-05 G) through relay optics. When the height of the objective lens was adjusted for the near field plane, the position of the lens was defined as z = 0 where NFP is observed. The beam profile was measured by acquiring the images after shifting the z position. The magnification of the objective lens was 10x (different from the previous work) due to measuring a wider range of images. The FFP was measured by a CCD camera (Hamamatsu ORCA-05 G) through FFP optics (Hamamatsu, A3267-12) designed for a wide angle with an appropriate neutral density filter (Hamamatsu, A7659-01) using a beam profiler (Hamamatsu, Lepas-12).
5. Result & discussion
5.1 Lasing characteristics
This section presents the typical lasing characteristics of the iPMSEL, including the light-current characteristics and lasing spectrum. The device we measured was based on the superimposing method. Figure 5(a) shows the light-current characteristics of the iPMSEL for room-temperature pulse operation, where the threshold current was 0.45 A and the slope efficiency was 0.20 W/A. The lasing spectrum for operation at 1.0 A is shown in Fig. 5(b), where we can see that it exhibited a narrow peak with a wavelength of 939.08 nm.
Fig. 5. Lasing characteristics of iPMSEL: (a) light-current output characteristics and (b) lasing spectrum.
5.2 Focusing profile
The focusing profile of the iPMSEL based on the superimposing method is shown in Fig. 6(a). Note that the exposure time of the CCD camera and neutral density filter were fixed at the near field plane (z = 0 mm) of each focusing profile. The beam pattern was set to focus on z = 1.00 mm and z = 2.00 mm. The horizontal position of the focal point from the center on z = 1.00 mm was x = 87.6 µm, while that on z = 2.00 mm was x = –177.3 µm. Because the Fourier transformation of exp(jϕPattern) is expanded by factor λf in the Xd- and Yd-axes on the focal plane (see Supplement 1), the position of the focusing beam where the in-plane component of wavevector k equals (kx, ky) is given by
According to the in-plane component of wavevectors k1 = (0.095,0) µm-1 on z = 1 mm, k2 = (–0.095,0) µm-1 on z = 2.00 mm, and the wavelength λ = 940 nm, the horizontal position of the focal point on z = 1.00 mm was calculated as x = 89.3 µm while that on z = 2.00 mm was x = –178.6 µm. Therefore, the experimental positions are in good agreement with the theoretical estimation. Note that the focusing patterns also accompanied the defocusing patterns on z = 1.00 mm and z = 2.00 mm, as the difference between the two focal lengths was too small to separate the beam waists from each other.
Fig. 6. Focusing profiles of simple 3D hologram for (a) superimposing method and (b) random tiling method. X-Z cross-sections of (c) superimposing method and (d) random tiling method.
The focusing profile of the iPMSEL based on the random tiling method exhibited the same tendency, as shown in Fig. 6(b). The horizontal position of the focal point from the center on z = 1.00 mm was x = 86.6 µm while that on z = 2.00 mm was x = –175.0 µm. These results are also in good agreement with the theoretical estimation. Therefore, both methods successfully demonstrate the desired focusing profile, where focus points are set at z = 1.00 mm and z = 2.00 mm. The in-plane position of the focal points is also in good agreement with the theoretical estimation. For intuitive understanding, the X-Z cross-sections of both focusing profiles, which were acquired with a 50-µm spacing in the Z-axis, are also shown in Fig. 6(c)–(d). We can see a slight difference between the superimposing method and the random tiling method here: the random tiling method tended to suppress all beam patterns except for focusing beams. This is possibly because diffraction in a particular direction didn’t occur due to the spatial randomness. The details of the focusing profiles are provided in S3 and two movie files (Visualization 1 and Visualization 2). Theoretical consideration of the focusing profiles are given in S5.
5.3 Far field pattern
The FFPs of the iPMSEL based on the superimposing method and the random tiling method are shown in Fig. 7(a) and (b), respectively. Doubly overlapped square patterns whose centers coincide at around (±5°, 0) were observed in both methods. Because the symmetric far field patterns were obtained in the iPMSEL due to the in-plane counter propagating lightwaves in the lasing cavity, the doubly overlapped square patterns were the overlap of the ±1st order beams (see Supplement 1). The narrower and wider square patterns correspond to the focusing beam at z = 2 mm and z = 1 mm, respectively. Twin spot noise beams were observed at (±15.5°, 0) in both methods: quite strongly in the superimposing method and more faintly in the random tiling method. A theoretical consideration suggests that this stems from the interference between focusing beams with different focal lengths (see Supplement 1). In fact, the 3D hologram with multiple points and a single focal length didn’t cause the spot noise beam; the diffraction in a particular direction was suppressed in the case of the random tiling due to spatial randomness, while the interference between focusing beams with a different focal length occurred. Note that the 3D hologram based on the superimposing method consists of higher order beams including the original hologram due to the manner of the holography, as discussed in S4. Moreover, the higher order beams appeared strongly near the position of the interference between focusing beams with a different focal length. Although the higher order beams without the original hologram and the spot noise beams were hindered (Fig. 7(a)) due to the neutral density filter, these noise beams in the superimposing method may cause overexposure at unexpected positions, especially when used in narrow regions such as the in-vivo environment. In contrast, higher order beams were not present in the random tiling method, and the spot noise beams were suppressed due to the spatial randomness, which may weaken the interference between focusing beams with different focal lengths.
6. Demonstration of 3D hologram with multiple points and multiple focal lengths
In this section, we demonstrate a more complex 3D hologram with multiple points and multiple focal lengths. The schematics of the output beam are shown in Fig. 8(a)(b). The structure of the device was the same as that in Fig. 1 except for the holographic design. The output beam was designed as one-dimensional (1D) aligned focusing dots patterns with spacing at focal lengths of z = 1 mm and 2 mm. Both line dot patterns were crossing orthogonally. The design procedure was the same as that in Section 3. The phase distributions of the 3D hologram based on the superimposing method and the random tiling method are shown in Fig. 8(c) and (d), respectively, and their focusing profiles are shown in Fig. 9(a), (b). Both holograms exhibited the desired focusing profiles. Note that in both cases the noise beam patterns are not noticeable (in contrast to the previous simple 3D hologram) because there were too many pattern points to recognize a particular interference.
Fig. 8. Schematics of device structure. (a) Perspective view, (b) cross-sectional view, (c) phase distribution based on superimposing method, and (d) phase distribution based on random tiling method.
Fig. 9. Focusing profile of complex 3D hologram: (a) superimposing method and (b) random tiling method.
7. Summary
Toward the generation of 3D holograms from on-chip size surface-emitting lasers utilizing a holographically modulated photonic crystal cavity, we examined the 3D hologram for two cases: a simple case featuring two different focal lengths with a single off-axis point in each and a more typical case with multiple points and multiple focal lengths. Two types of holography, one based on superimposition and the other on random tiling, successfully demonstrated the desired focusing profiles. In the far field plane, the simple 3D hologram explicitly caused a spot noise beam due to the interaction between 3D holograms with different focal lengths. This beam was significant in the superimposing method and fainter in the random tiling method due to spatial randomness, which does not cause diffraction in a particular direction. We also found that the 3D hologram based on the superimposing method consisted of higher order beams including the original hologram due to the manner of the holography. These noise beam patterns were not noticeable in the far field plane because there were too many pattern points to recognize a particular interference. Note that these patterns should be considered because they can cause severe overexposure at unexpected positions, such as the narrow region utilized in the in-vivo environment. Overall, we demonstrated for the first time that 3D holograms with multiple points and multiple focal lengths can be directly generated from on-chip size surface-emitting lasers. We believe our findings will bring innovation to mobile optical systems that suffer from the size of the total system, complicated combinations of optical elements, and a lack of robustness to mechanical vibration. This will ultimately pave the way to developing compact optical systems in areas such as material processing, micro fluidics, optical tweezers, and endoscopy.
Funding
Center of Innovation Program (JPMJCE1311); Japan Science and Technology Agency.
Acknowledgments
The authors are grateful to A. Hiruma, H. Toyoda, T. Hara, M. Niigaki, Y. Yamashita, K. Nozaki, and T. Edamura of HPK for their encouragement throughout this work. We also thank A. Higuchi and M. Hitaka for their assistance with the epitaxial growth.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. W. W. Chow, S. W. Koch, and M. Sargent III, “Semiconductor-laser physics,” (Springer, 1994).
2. M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (1999). [CrossRef]
3. K. Hirose, Y. Liang, Y. Kurosaka, A. Watanabe, T. Sugiyama, and S. Noda, “Watt-class high-power, high-beam-quality photonic-crystal lasers,” Nat. Photonics 8(5), 406–411 (2014). [CrossRef]
4. M. Yoshida, M. D. Zoysa, K. Ishizaki, Y. Tanaka, M. Kawasaki, R. Hatsuda, B. Song, J. Gelleta, and S. Noda, “Double-lattice photonic-crystal resonators enabling high-brightness semiconductor lasers with symmetric narrow-divergence beams,” Nat. Mater. 18(2), 121–128 (2019). [CrossRef]
5. R. Morita, T. Inoue, M. D. Zoysa, K. Ishizaki, and S. Noda, “Photonic-crystal lasers with two-dimensionally arranged gain and loss sections for high-peak-power short-pulse operation,” Nat. Photonics 15(4), 311–318 (2021). [CrossRef]
6. T. Inoue, M. Yoshida, J. Gelleta, K. Izumi, K. Yoshida, K. Ishizaki, M. D. Zoysa, and S. Noda, “General recipe to realize photonic-crystal surface-emitting lasers with 100-W-to-1-kW single-mode operation,” Nat. Commun. 13(1), 3262 (2022). [CrossRef]
7. T. Okino, K. Kitamura, D. Yasuda, Y. Liang, and S. Noda, “Position-modulated photonic-crystal lasers and control of beam direction and polarization,” in CLEO: 2015, paper SW1F.1.
8. S. Noda, K. Kitamura, T. Okino, D. Yasuda, and Y. Tanaka, “Photonic-Crystal Surface-Emitting Lasers: Review and Introduction of Modulated-Photonic Crystals,” IEEE J. Sel. Top. Quantum Electron. 23(6), 1–7 (2017). [CrossRef]
9. R. Sakata, K. Ishizaki, M. D. Zoysa, S. Fukuhara, T. Inoue, Y. Tanaka, K. Iwata, R. Hatsuda, M. Yoshida, J. Gelleta, and S. Noda, “Dually modulated photonic crystals enabling high-power high-beam-quality two-dimensional beam scanning lasers,” Nat. Commun. 11(1), 3487 (2020). [CrossRef]
10. B. R. Brown and A. W. Lohmann, “Complex Spatial Filtering with Binary Masks,” Appl. Opt. 5(6), 967–969 (1966). [CrossRef]
11. A. W. Lohmann and D. P. Paris, “Binary Fraunhofer Holograms, Generated by Computer,” Appl. Opt. 6(10), 1739–1748 (1967). [CrossRef]
12. B. R. Brown and A. W. Lohmann, “Computer-generated Binary Holograms,” IBM J. Res. Dev. 13(2), 160–168 (1969). [CrossRef]
13. Y. Kurosaka, K. Hirose, T. Sugiyama, Y. Takiguchi, and Y. Nomoto, “Phase-modulating lasers toward on-chip integration,” Sci. Rep. 6(1), 30138 (2016). [CrossRef]
14. Y. Takiguchi, K. Hirose, T. Sugiyama, Y. Nomoto, S. Uenoyama, and Y. Kurosaka, “Principle of beam generation in on-chip 2D beam pattern projecting lasers,” Opt. Express 26(8), 10787–10800 (2018). [CrossRef]
15. K. Hirose, Y. Takiguchi, T. Sugiyama, Y. Nomoto, S. Uenoyama, and Y. Kurosaka, “Removal of surface-normal spot beam from on-chip 2D beam pattern projecting lasers,” Opt. Express 26(23), 29854–29866 (2018). [CrossRef]
16. Y. Kurosaka, K. Hirose, A. Ito, M. Hitaka, A. Higuchi, T. Sugiyama, Y. Takiguchi, Y. Nomoto, S. Uenoyama, and T. Edamura, “Beam Pattern Projecting On-Chip Lasers at Visible Wavelength,” in CLEO: 2019, paper SM4N.2.
17. K. Hirose, H. Kamei, T. Sugiyama, and Y. Kurosaka, “200×200 μm2 structured light source,” Opt. Express 28(25), 37307–37321 (2020). [CrossRef]
18. Y. Kurosaka, K. Hirose, H. Kamei, and T. Sugiyama, “Replication of band structure in an arbitrary wave vector by holographic modulation,” Phys. Rev. B 103(24), 245310 (2021). [CrossRef]
19. M. Li, J. Bengtsson, M. Hagberg, and A. Larsson, “Off-plane computer-generated waveguide hologram,” IEEE J. Quantum Electron. 2(2), 226–235 (1996). [CrossRef]
20. Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave model for square-lattice photonic crystal lasers with transverse electric polarization: A general approach,” Phys. Rev. B 84(19), 195119 (2011). [CrossRef]
21. Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave analysis for square-lattice photonic crystal surface emitting lasers with transverse-electric polarization: finite-size effects,” Opt. Express 20(14), 15945–15961 (2012). [CrossRef]
22. J. Goodman, Introduction to Fourier Optics, 3rd ed, (Roberts & Co Publishers, 2005), Chap. 3-5.
23. K. Hirose, H. Kamei, and T. Sugiyama, “Direct-focusing surface-emitting laser,” Opt. Express 30(2), 3066–3075 (2022). [CrossRef]
24. K. Hirose, K. Watanabe, H. Kamei, T. Sugiyama, Y. Takiguchi, and Y. Kurosaka, “On-chip size, low-noise fringe pattern projector offering highly accurate 3D measurement,” Opt. Lett. 48(6), 1387–1390 (2023). [CrossRef]
25. Y. Ichioka, M. Izumi, and T. Suzuki, “Scanning Halftone Plotter and Computer-Generated Continuous-Tone Hologram,” Appl. Opt. 10(2), 403–411 (1971). [CrossRef]
26. J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. 32(8), 912–914 (2007). [CrossRef]
27. A. Vijayakumar, T. Katkus, S. Lundgaard, D. P. Linklater, E. P. Ivanova, S. H. Ng, and S. Juodkazis, “Fresnel incoherent correlation holography with single camera shot,” Opto-Electron. Adv. 3(8), 200004 (2020). [CrossRef]
28. S. Sakamaki, N. Yoneda, and T. Nomura, “Single-shot in-line Fresnel incoherent holography using a dual-focus checkerboard lens,” Appl. Opt. 59(22), 6612–6618 (2020). [CrossRef]
29. R. W. Gerchberg and W. O. Saxton, “A Practical Algorithm for the Determination of Phase from Image and Diffraction Plane Pictures,” Optik 35, 237–246 (1972).
30. J. R. Fienup, “Phase retrieval algorithms: A comparison,” Appl. Opt. 21(15), 2758–2769 (1982). [CrossRef]
31. O. Ripoll, V. Kettunen, and H. P. Herzig, “Review of iterative Fourier-transform algorithms for beam shaping applications,” Opt. Eng. 43(11), 2549–2556 (2004). [CrossRef]
