Coded Aperture Correlation Holography

From the observation of stars to microbes, advancements in digital holography could bring wide-scale improvements to imaging technology.

VIJAYAKUMAR ANAND, SWINBURNE UNIVERSITY OF TECHNOLOGY, AND JOSEPH ROSEN, BEN-GURION UNIVERSITY OF THE NEGEV

Coded aperture correlation holography (COACH) is a recently developed 3D-imaging technology. It began as a regular in-line, two-beam interference holography and has evolved into an interferenceless technique based on a working principle entirely different from techniques of conventional holography. A system is calibrated using a one-time “COACHing” procedure, which records the point spread function (PSF) library along the depth. Then, an object is placed within the calibrated object space and one or more intensity patterns are recorded. The various planes of an object are reconstructed by a computational cross-correlation between the PSF library and the object intensity pattern. The capabilities of COACH improve upon most facets of equivalent regular imaging systems, and its requirements are minimal.

Digital imaging and holography

Observation is the first step along the path of understanding the world around us, and imaging is one of our main tools. Imaging technology is the collection of methods used to create or gather images in one domain and duplicate them in another. Currently, we are in an era in which images are recorded by digital cameras and processed by computer software.

Digital holography is a well-known example of 3D imaging in which the camera records one or more holograms of an observed scene. A classical digital hologram is a pattern of light intensity created by interference of light beams, with at least one of the beams containing the information of the observed object. The image, usually a 3D depiction of the scene, is reconstructed by the computer program. The main benefit of digital holography is the ability to capture 3D scenes with a single camera shot, or very few camera shots. Other advantages include the ability to image targets through a scattering medium, and the ability to resolve object details better than imaging systems that have an equivalent physical aperture.

To bring I-COACH from the research lab to industry, assistive technologies such as mobile computation and add-on gadgets will be needed, in addition to optimization processes for large-scale manufacturing of the coded masks.

Many imaging tasks in optics are performed with natural incoherent light. This is true for most microscopes, all telescopes, and numerous other imaging devices. However, neither classical holography in general nor digital holography in particular are widely applied to general natural light imaging. This is because the creation of holograms requires a coherent interference system in which two coherent laser beams interfere to create the hologram’s pattern. Possible solutions to detour this coherence problem include Fresnel incoherent correlation holography (FINCH)¹ and the more general technique known as COACH². In both techniques, the input beam is detected by a digital camera after the beam passes through one or more optical masks. As in the case of digital holography, the observed object is reconstructed by a digital algorithm. However, the two techniques are not restricted to coherence requirements between reference and object beams.

Imaging evolution

The historical roots of FINCH and COACH are planted in coded aperture imaging (CAI) technology, which dates to the 1960s. In CAI, a random array of pinholes is used to replace the single pinhole in lensless pinhole cameras to obtain an increased throughput and a higher signal-to-noise ratio (SNR)³. CAI generates a random distribution of images corresponding to every location of the pinhole, resulting in an enhanced light throughput, unlike the single weak image generated by the single pinhole. However, reconstructing the image of the object from the recorded intensity pattern of the superposed images is more difficult than imaging with a single pinhole. A PSF is recorded using a point object at the exact location of the object and with the same pinhole array. The image of the object is reconstructed by a cross-correlation between the object intensity and the PSF. Because of the difficulty of manufacturing lenses for nonvisible bands of the electromagnetic spectrum, this method of correlation-based imaging has served the purpose of imaging without lenses.

The concept of imaging based on correlation can be understood from a fundamental optical configuration (Figure 1). A point object is imaged at various random locations as point images corresponding to the locations of the pinholes in the array. When the point object is replaced by a multipoint object such as a smiley (Figure 1a), the images of the smiley are replicated at the locations of the point images on the sensor plane. In experiments, the point spread intensity pattern and the object intensity pattern were obtained for a random array of 50 and 100 pinholes (Figures 1b and 1c). Based on the resulting images, it is impossible to know the image of the object when the number of pinholes increases, although the fundamental building block of the intensity pattern is the image of the object itself.

Figure 1. Optical configuration of imaging using a random pinhole array (a). Images of the array, PSF, object intensity patterns, and reconstruction for 50 pinholes (b) and 100 (c). Courtesy of Vijayakumar Anand and Joseph Rosen.

In 2011, Wanli Chi and Nicholas George reopened the topic of CAI by demonstrating 2D imaging with a phase-only spatial light modulator (SLM)⁴. In principle, the idea was similar to CAI but in a more generalized version, where instead of a random array of point images, a chaotic intensity pattern was generated for a point object. For a multipoint object, a chaotic intensity pattern was generated for every object point and superposed on the sensor plane. The image of the object was reconstructed by a cross-correlation, as described previously. While the cross-correlation principle was the same as CAI, the light throughput increased because of the use of a phase aperture. Additionally, the SNR decreased because the light spread over a wide chaotic intensity pattern instead of being focused into a relatively small number of randomly distributed dots.

COACH and FINCH

COACH was developed in 2016² as a generalization and an alternative to the well-established FINCH¹. The optical configurations of the two techniques are compared in Figure 2. Unlike the random array of pinholes of CAI, or the phase-coded aperture introduced by Chi and George, COACH and FINCH are self-interference-based 3D-imaging methods. An object wave is split into two, and one of the waves is modulated by a quadratic phase mask (FINCH) or a random-like coded phase mask (COACH), and interfered with the unmodulated object wave on the image sensor.

Figure 2. Optical configurations for FINCH (a) and COACH (b). Courtesy of Vijayakumar Anand and Joseph Rosen.

Figure 2. Optical configurations for FINCH (a) and COACH (b). Courtesy of Vijayakumar Anand and Joseph Rosen.

The use of incoherent illumination maintains the same operating principle for both techniques. For any object point, a two-beam interference pattern such as a circular fringe pattern (FINCH) or a chaotic pattern (COACH) is formed. A multipoint object produces an interference pattern for every object point in both cases. The intensity pattern recorded by the sensor is the accumulation of such interference patterns for every object point. In FINCH, recording of the PSF can be avoided and the image of the object can be reconstructed by propagating the hologram digitally (with a computer program) to the image plane. The reconstruction in COACH is similar to the earlier studies involving a cross-correlation between the object hologram and the PSF. However, COACH has 3D-imaging capability achieved by recording PSFs at various axial locations and reconstructing the object images at various planes.

Since FINCH and COACH are in-line holography techniques, they require at least three phase-shifted camera shots to reconstruct the 3D image without twin-image and bias terms. On the one hand, even though FINCH exhibits a higher lateral resolution beyond the Abbe diffraction limit, it has a lower axial resolution. COACH, on the other hand, has a higher axial resolution and a lower lateral resolution. From a 3D-imaging perspective, COACH has numerous advantages. The results of imaging two smiley objects located at two different axial planes using the direct imaging techniques of FINCH and COACH are shown in Figure 3. FINCH shows a lower axial resolution but better SNR and lateral resolution.

Figure 3. Images of two smileys located at different axial planes, with the positive smiley (a) and the negative smiley (b) in focus. Phase (c) and intensity (d) of the complex FINCH object hologram. Reconstruction results of FINCH with the propagation distance of the positive smiley (e) and negative smiley (f). Phase (g) and intensity (h) of the complex COACH object hologram. Reconstruction results of COACH with the PSF recorded at the distances of the positive smiley (i) and negative smiley (j). Phase (k) and intensity (l) of the PSF where the point object is located at the plane of the positive smiley. Phase (m) and intensity (n) of the PSF where the point object is located at the plane of the negative smiley. The two objects when located in the same plane (o) and the phase mask displayed on the SLM of COACH (p). Courtesy of Vijayakumar Anand and Joseph Rosen.

Further studies on COACH resulted in the development of an interferenceless COACH (I-COACH) technique, where 3D imaging was achieved without two-beam interference⁵ and by recording a PSF library only once. Because I-COACH is an indirect imaging technique based on correlation, several techniques were developed in subsequent studies to improve its spectral resolution, time resolution, field of view, lateral and axial resolutions, and SNR⁶. Other capabilities include imaging through partial aperture, through scattering medium, in a mode of synthetic aperture, and without refractive lenses6.

Most versions of I-COACH mentioned in the studies6 need at least two camera shots. The nonlinear correlation technique was developed to reconstruct the image of the object with a single camera shot and with high SNR. Alternative methods — such as a phase-only filter, a Wiener filter, and a Lucy-Richardson algorithm — reconstructed images with an improved SNR, but could not reach the SNR level of the nonlinear correlation and required more than one camera shot7. Nonlinear correlation is a method where the magnitudes of the spatial spectrums of the two correlated functions are raised to the power of a number between −1 and 1 until a high SNR (quantified by a measure of the least entropy) is obtained. The nonlinear correlation was found to be a reliable and adaptive reconstruction tool in comparison to the above-mentioned filters and algorithms⁷. The latest study in this line of research revealed that the SNR can be controlled by returning to the earlier PSF of randomly distributed dots, but this time with the phase-coded aperture instead of a pinhole array⁸.

Recent advancements in the area of COACH make the technique attractive for commercialization6,8. With the development of smartphone-based microscopy techniques, it is possible to convert this research into low-cost, reliable, and compact imaging systems. The low-cost aspect of I-COACH can be attributed to the following factors: 1) it requires only an LED, which is less expensive compared to coherent sources; 2) it does not require active devices such as spatial light modulators — only a random phase mask, which can be fabricated, or a diffuser sheet; 3) it is a motionless technique and therefore does not require any expensive optomechanical components; and, above all, 4) it is an interferenceless, nonscanning technique that does not require the vibration isolation required for most holographic imagers.

For these reasons, I-COACH may be an attractive candidate for commercialization in the target areas of fluorescence microscopy, astronomy, biomedical imaging, and hyperspectral imaging. At the same time, I-COACH products can be realized at a reduced cost compared to existing holographic-based imaging technologies available in the market. The technique will bring an excellent scope of products to the imaging market in the coming years. However, to bring I-COACH from the research lab to industry, assistive technologies such as mobile computation and add-on gadgets will be needed, in addition to optimization processes for large-scale manufacturing of the coded masks.

Meet the authors

Vijayakumar Anand is a nanophotonics research fellow at the Center for Microphotonics at Swinburne University of Technology in Melbourne, Australia. His research interests include digital holography, imaging, diffractive optics, spectroscopy, and microfabrication.

Joseph Rosen is a professor and the Benjamin H. Swig optoelectronics chair at Ben-Gurion University of the Negev in Beer-Sheva, Israel. He is a fellow of OSA and SPIE.

References

1. J. Rosen and G. Brooker (2007). Digital spatially incoherent Fresnel holography. Opt Lett, Vol. 32, Issue 8, pp. 912-914.

2. A. Vijayakumar et al. (2016). Coded aperture correlation holography — a new type of incoherent digital holograms. Opt Express, Vol. 24, Issue 11, pp. 12430-12441.

3. J.G. Ables (1968). Fourier transform photography: a new method for x-ray astronomy. Proc Astron Soc Aust, Vol. 1, pp. 172-173.

4. W. Chi and N. George (2011). Optical imaging with phase-coded aperture. Opt Express, Vol. 19, Issue 5, pp. 4294-4300.

5. A. Vijayakumar and J. Rosen (2017). Interferenceless coded aperture correlation holography — a new technique for recording incoherent digital holograms without two-wave interference. Opt Express, Vol. 25, Issue 12, pp. 13883-13896.

6. J. Rosen et al. (2019). Recent advances in self-interference incoherent digital holography. Adv Opt Photon, Vol. 11, Issue 1, pp.1-66.

7. A. Vijayakumar et al. (2019). Implementation of a speckle-correlation-based optical lever with extended dynamic range. Appl Opt, Vol. 58, Issue 22, pp. 5982-5988.

8. M.R. Rai and J. Rosen (2019). Noise suppression by controlling the sparsity of the point spread function in interferenceless coded aperture correlation holography (I-COACH). Opt Express, Vol. 27, Issue 17, pp. 24311-24323.