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Spectrum and space resolved 4D imaging by coded aperture ... rosen/4D imaging COACH ol.pdfSpectrum and space resolved 4D imaging by coded aperture correlation holography (COACH) with
Spectrum and space resolved 4D imaging by coded aperture ... rosen/4D imaging COACH ol.pdfSpectrum and space resolved 4D imaging by coded aperture correlation holography (COACH) with
Spectrum and space resolved 4D imaging by coded aperture ... rosen/4D imaging COACH ol.pdfSpectrum and space resolved 4D imaging by coded aperture correlation holography (COACH) with
Spectrum and space resolved 4D imaging by coded aperture ... rosen/4D imaging COACH ol.pdfSpectrum and space resolved 4D imaging by coded aperture correlation holography (COACH) with
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  • Spectrum and space resolved 4D imaging bycoded aperture correlation holography (COACH)with diffractive objective lensA. VIJAYAKUMAR* AND JOSEPH ROSENDepartment of Electrical and Computer Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 8410501, Israel*Corresponding author: physics.vijay@gmail.com

    Received 30 December 2016; revised 30 January 2017; accepted 6 February 2017; posted 9 February 2017 (Doc. ID 283867);published 24 February 2017

    In this Letter, we present an advanced optical configurationof coded aperture correlation holography (COACH) with adiffractive objective lens. Four-dimensional imaging of ob-jects at the three spatial dimensions and with an additionalspectral dimension is demonstrated. A hologram of three-dimensional objects illuminated by different wavelengths wasrecorded by the interference of light diffracted from the objectswith the light diffracted from the same objects, but through arandom-like coded phase mask (CPM). A library of hologramsdenoted point spread function (PSF) holograms were prere-corded with the same CPM, and under identical conditions,using point objects along different axial locations and for thedifferent illuminating wavelengths. The correlation of theobject hologram with the PSF hologram recorded using a par-ticular wavelength, and at a particular axial location, recon-structs only the object corresponding to the particular axialplane and to the specific wavelength. The reconstruction re-sults are compared with regular imaging and with anotherwell-established holographic technique called Fresnel incoher-ent correlation holography. 2017 Optical Society of America

    OCIS codes: (100.6640) Superresolution; (090.1995) Digital hologra-

    phy; (110.0110) Imaging systems; (110.0180) Microscopy; (090.1760)

    Computer holography; (050.5080) Phase shift.


    Holography, invented by Dennis Gabor, revolutionized thefield of imaging by introducing the possibility of recording andreconstructing three-dimensional (3D) spatial information ofobjects [1,2]. Digital holography, the modern technique ofholography, has replaced regular imaging in numerous applica-tions due to its various advantages [36]. Capturing, and stor-ing on a hologram, information from additional dimensionsbeyond the well-known three spatial dimensions can be usefulfor various applications. Digital holographic techniques havebeen developed in the recent years for recording and reconstruct-ing information beyond the three spatial dimensions [712].

    A unique digital holographic technique termed Fresnel inco-herent correlation holography (FINCH) using incoherent light

    was invented in 2007 [13,14]. FINCH is classified in the cat-egory of self-informative reference holography, in which thelight diffracted by every point on the object under study is in-terfered with itself, and both interfering beams contain theinformation of the point location. This self-interference effectin FINCH has pushed its lateral resolution limits beyond theclassical limits dictated by the Lagrange invariant law [1519].However, the axial resolution of FINCH was found to be lowerthan that of regular imaging. In this line of research, a usefulincoherent self-referenced digital holographic system dubbedcoded aperture correlation holography (COACH) has been de-veloped most recently [20]. Due to the use of a random-likecoded phase mask (CPM), instead of the quadratic phase maskof FINCH, the axial resolution has been improved [20]. COACHwas found to possess axial and lateral resolutions similar to that ofan equivalent regular imaging system but, unlike the last one, asingle hologram of COACH has the capability of recording andreconstructing 3D scenes. One of the limitations of COACH wasthe inherent background noise generated during reconstruction.Different noise reduction techniques such as phase-only filtering,averaging and hybridization techniques were developed to mini-mize the background noise generated in COACH [21].

    In this Letter, we present an advanced configuration ofCOACH for recording and reconstructing objects with spatial,as well as spectral information and, thus, the system demon-strates four-dimensional (4D) imaging. Recording and recon-structing the additional spectral information can be usefulfor hyperspectral imaging as well as for imaging spectrometer[22]. The high axial resolution of COACH arising from therelatively short axial correlation lengths of the random-likeCPM is exploited to extend the information acquisition in or-der to resolve not only spatial, but also spectral information.

    The optical configuration of 4D-COACH is shown in Fig. 1.The description is given for only two wavelengths, although itcan be straightforwardly generalized for polychromatic light. Thelight from two incoherent sources of different wavelengths isfocused to critically illuminate [23] two different axial planes ofa multiplane object. The beams with two wavelengths 1 and 2diffracted from different planes of the object are incident on adiffractive lens (DL) of focal length f 1 mounted at a distance

    Letter Vol. 42, No. 5 / March 1 2017 / Optics Letters 947

    0146-9592/17/050947-04 Journal 2017 Optical Society of America


  • f 1 from the object. The DL is sensitive to wavelengths and,thus, the focal distance of the DL is different for different wave-lengths. Hence, even when both the wavelengths illuminate thesame axial plane of the object, they are focused at different dis-tances due to the dispersion of the DL. Since all sources arespatially incoherent, the light emitted by each object point witha specific wavelength is coherent only with itself and, therefore,can only interfere with itself. The beam diffracted by the DL ispolarized by polarizer P1 oriented at 45 with respect to theactive axis of the spatial light modulator (SLM). Similar to [20],a random-like CPM, calculated using the GerchbergSaxtonalgorithm [24,25] to obtain uniform intensity in the spectrumdomain, is displayed on the SLM. As the polarization of thecollimated light is oriented at 45 with respect to the active axisof the SLM, only about half of the intensity of the incident lightis modulated by the phase profile displayed on the SLM. Theremaining half of the intensity passes through the SLM withoutany modulation. A second polarizer P2 also oriented 45 withrespect to the active axis of the SLM projects the modulatedand the unmodulated components onto the same orientationsuch that the beams interfere on the sensor plane. This multi-plexing scheme adapted from [26] allows the generation of twointerfering beams in a compact single channel optical configu-ration. The twin image and the bias terms present in the holo-gram are cancelled out by a phase-shifting procedure involvingrecording of three holograms corresponding to the three phasevalues 0, 120, and 240 followed by their superposition[13]. A library of complex holograms dubbed PSF hologramsHPSF; z is synthesized from three phase-shifting holograms.These PSF holograms are recorded by shifting a pinhole alongall possible axial locations of objects and by illuminating thepinhole with entire wavelengths used in the setup. The libraryHPSF; z is prepared once and is later used for any number oftimes for reconstructing the entire object holograms. Once thelibrary is ready for use, the pinholes are replaced by objects, andcomplex holograms of the 3D objects, named H object, are re-corded by the same phase-shifting process. In the previousCOACH [20,21], the correlation of H object with the library ofHPSFs yields the images at exactly the original axial locations.However, in the present configuration with the DL, the spatialinformation of the object, as well as the wavelength illumination,can be extracted. Hence, it is possible to acquire spatial, as well asspectral, information about the object using the 4D-COACHtechnique. In other words, the HPSFs of different wavelengthscan be used to demultiplex the specific wavelength informationfrom the object hologram, in addition to the spatial information.

    The wavelength sensitivity of the different systems FINCH,COACH, and regular imaging with a refractive lens and a DLwas studied by simulating the beam propagation in the respec-tive systems under identical conditions similar to the experi-mental setup. A detailed description of the HPSFs calculationis presented in [20,21]. The reference hologram HPSF was re-corded for 633 nm, and it was correlated with HPSFs re-corded for different wavelengths from 534 to 733 nm. Thenormalized intensity of the image at x; y 0; 0 is calcu-lated for each imaging method. The plots of the point imageintensity at x; y 0; 0 versus the wavelength of the sourcefor COACH, FINCH, and regular imaging are plotted inFig. 2. The graphs of COACH and regular imaging in Fig. 2can be explained using the model of transmission of a Gaussianbeam through a thin lens [27]. In the case of regular imagingwith a refractive objective lens, there is only a single DL whichis displayed on the SLM. The focal distance of this DL isf R, where R is the radius of the DL, and is the small-est cycle of the DL. The differentiation of f with respect to ,and the substitution of f R yields the expression f f for any change of the focal distance due to wavelengthchange . The width of the intensity curve I near the focalpoint is obtained by comparing f to the width of the axialfocus curve, given by [27], z 2f 2R2. Following thiscalculation, the width of the curve I is 22f R2.When the diffractive objective lens replaces the refractive ob-jective lens, the sensitivity of each DL to the wavelength is sim-ilar but the final curve I is obtained as a product of twoLorenzians, each of which is contributed by one of t

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