Techniques of self-interference incoherent digital holography

Transcription

1 Technques of self-nterference ncoherent dgtal holography Invted Paper Davd C. Clark and Myung K. Km Department of Physcs Unversty of South Florda Tampa, U.S.A. Abstract We dscuss and demonstrate our recent developments usng self-nterference ncoherent dgtal holography to brdge the gap between ndspensable ncoherent magng technques and the advantages of three-dmensonal holographc recordng. We demonstrate the ablty to record broadband sunlt photographc holograms, apply non-nvasve three-dmensonal trackng technques, and the ease of adaptaton to exstng tools n mcroscopy and fluorescence. Keywords ncoherent holography; dfferental magng; fluorescence mcroscopy; three-dmensonal trackng I. INTRODUCTION Image recordng usng ncoherently llumnated objects and specmens s wdely used due to mmedate and low cost source lght avalablty. Wthout the use of technques such as confocal pont scannng, however, only two-dmensonal (2D) mages are captured. In contrast, holography records suffcent nformaton to recreate the three-dmensonal (3D) optcal feld emanatng from the scene, ncludng both ampltude and phase [1]. The three-dmensonal recordng s made possble by the nterference of the object s optcal feld and a reference optcal feld, and therefore requres coherence between the two. In D. Gabor s orgnal concepton, the reference s realzed from a part of the llumnaton undsturbed by the object [2]. The nventon of the laser made t possble to provde a coherent reference feld explctly [3]. Because coherence s at the core of holography, recordng holograms under ncoherent llumnaton has been problematc untl recent advancements. The ntroducton of Fresnel ncoherent correlaton holography (FINCH) has fully demonstrated the ablty to generate holographc mages of ncoherent object felds, ncludng 3D fluorescence mcroscopy [4,5]. In ths technque, two copes of the object wave are superposed wth dfferent phase factors mposed by a spatal lght modulator (SLM), so that every pont source on the object produces the Fresnel zone nterference pattern [6]. We have snce developed a technque conceptually smlar to FINCH called selfnterference ncoherent dgtal holography (SIDH), n whch the SLM s replaced by a modfed Mchaelson nterferometer wth a dfferental phase curvature appled by ts two mrrors [7]. For contnuous objects or scenes, the spatal ncoherence of the object ponts leads to rapd buld-up of ncoherent background whch s removed by standard phase-shftng dgtal holography [8]. The resultant hologram can then be numercally propagated to any dstance to reconstruct the desred optcal feld. Because coherence length s nversely proportonal to bandwdth, broadband ncoherent llumnated subjects present a notable challenge whch s overcome by our SIDH process. We dscuss here our recent developments related to our method of SIDH ncludng 3D holographc photography, dfferental self-nterference ncoherent dgtal holography (dff-sidh), and holographc mcroscopy all nvolvng completely spatally ncoherent llumnaton. We frst fully demonstrate SIDH and dff-sidh on photo-qualty holograms of unfltered broadband natural sunlt objects. We then demonstrate the easy adaptaton to commercal grade mcroscopy equpment, successfully convertng a professonal 2D magng nstrument nto a powerful 3D magng and Fg. 1. Expermental dagram for dff-sidh. An nput lens, L n, projects objects n the depth feld of vew, DFOI, nto the ntermedate mage space as nput to the SIDH module. The SIDH module conssts of a relay lens, L r, an rs, P, a beam spltter, BS, a flat pezo-mounted mrror, M a, a curved mrror, M b, and a CCD camera.

2 trackng tool. II. EXPERIMENTS A. Self-nterference Incoherent Dgtal Holography A basc SIDH confguraton s represented n Fg. 1. It conssts of the nput lens, the relay lens, the nterferometer, and a CCD array. The nput lens produces an ntermedate mage space as the nput for the SIDH module. The relay lens s selected and postoned to create an approprate fnal mage space relatve to the CCD plane. The nterferometer conssts of a beam-splttng cube and two mrrors. One s a plane mrror mounted on a pezo-actuator, whch s drven by a 5 volt ramp sgnal for phase-shftng. The other s a curved mrror to generate dfferental phase curvature. To ensure nterference, the dstances of the two mrrors are matched to wthn a margn based on the temporal coherence of the desred lght source [9]. The degree of ths adjustment s Fg. 2. Intal and fnal complex holograms. Chess peces, knght and kng, were arranged as shown n the ntal hologram, (a-c). The knght was then moved to a new poston and a fnal hologram was recorded, (d-f). (a), (b), and (c) are the same ntal hologram at the zero-plane (un-propagated), the knght plane, and the kng plane, respectvely. (d), (e), and (f) are the fnal hologram at the zero-plane, the kng plane, and the new knght plane, respectvely. vsbly verfed by magng a sngle ncoherent, out-of-focus, LED source for best frnge contrast. Then, several exposures of an ncoherent llumnated scene are captured whle the phase-shftng pezo-mounted mrror travels through at least one full 2 phase excurson. The complex hologram s calculated from these N ntensty profles, I n, by Fg. 3. Sunlt holographc recordng of chess set. (a) Out of focus hologram. (b) Same hologram numercally propagated to n-focus plane. (c) Cell phone camera mage of same scene for comparson. n 1 N 1 2 N H = I e n= 0 n. (1) N It s ths zero-plane (CCD-plane) complex hologram, now devod of DC and vrtual twn mages, that s used for further processng, such as dff-sidh or propagaton to reconstructon planes. A mnmum of N = 4 s requred to elmnate the unwanted terms; however, usng hgher values (up to 20 n cases presented here) ensures removal of DC sgnal and smooths random nose effects. Whle a detaled descrpton of the reconstructon s avalable n [7], we wll summarze here that our resultng complex holograms are smply propagated, as per dffracton theory, by desred dstances, z h, descrbed by zz a b zh = (2) za zb where z a,b are the axal postons of the fnal focal planes of a desred object plane through the two paths of the nterferometer and are measured relatve to the CCD plane.

3 For a well-defned system, these values are easly translated from object space to fnal mage space and back agan. For our purposes here, we use thn lens approxmated geometry, as well as compensaton for mage shft due to the 25.4 mm BK- 7 beam cube. An example of a broadband, sunlt hologram recorded usng SIDH s shown n Fg. 2 numercally propagated to and out-of-focus plane (a) and the n-focus plane (b) and a cell phone camera photo (c) s ncluded for comparson. B. Broadband Dfferental Incoherent Holography The process of dff-sidh s appled here to the case of chess peces on a chess board llumnated by sunlght through an offce wndow. A hologram s recorded of the ntal scene, Fg. 3(a-c). The knght was then moved to a new poston and a fnal hologram was recorded, Fg. 3(d-f). The dfference hologram s calculated from the un-propagated ntal and fnal complex holograms (Fg. 3(a) and (d), respectvely), H = H H. (3) f v = v v 2 1 = [ 5.4, 2.5, 62] mm [8.9,7.1, 0] mm = [ 14.3, 4.6, 62] mm for the knght s dsplacement vector n object space. It s mportant to consder the relatve locatons of subjects of nterest,.e., the depth feld of nterest (DFOI). Snce we are nterested n trackng objects n a 3D volume of space, our ntermedate mage space should consst of an approprate volume of space as nput for the dff-sidh system. In the above experment, the DFOI (spannng the length of the chess board) s between 350 mm and 430 mm from the relay lens. By thn lens geometry, ths translates to a 2.2 mm range n ntermedate mage space usng a negatve 75 mm nput lens placed 7 mm n front of the relay lens. Followng smlarly, the postve 50 mm relay lens of the SIDH module translates ths nput to a range of z a (plane mrror path) and z b (curved mrror path) values of 25.7 to 39.8 mm and 7.62 to 17.4 mm, respectvely. Thus applyng (2), we expect objects n our DFOI The resultng dfference hologram for ths experment s shown n Fg. 4(a-c) and contans the 3D optcal feld nformaton of the knght n both ntal and fnal postons, whle the unchanged nformaton, ncludng the statonary kng, are absent. As s shown, we numercally shft the focus of each hologram from ntal knght to kng to fnal knght postons (fgure 4(a-c), respectvely) to demonstrate that the 3D nformaton s preserved. It can also be notced that the nformaton on the chess board, both overlap and specular reflecton of the knght, s also preserved n a dfference hologram, snce ths represents changed nformaton as well. From ths sngle complex operaton, the overall volumetrc change of source ponts makng up the scene s computed and movement of object ponts n the scene s tracked n three dmensons. In the present case, f we select the eye of the knght as an easy pont of reference, a 3D dsplacement vector can be calculated showng the projected path between the tme of the ntal and fnal holograms. Usng the plane parallel to the CCD plane that contans the ntal eye as our reference and settng the orgn at the center of our feld of vew (FOV), poston vectors can be constructed from our dfference hologram for the ntal and fnal eye postons by px py v = [ x, y, z] (4) nx ny where px and py are the lateral pxel poston coordnates, nx and ny are the lateral FOV s n pxels, and x and y represent the object space FOV s n unts of length. Ths object space FOV s, of course, scaled based on the depth plane of nterest at z by the relaton z 0 = x0 z0 x z (and dentcally for y ) where x 0 s the known object space FOV at a plane located at z 0, and z s measured from ths z 0 plane and s translated from z h as descrbed n the followng paragraph. For our example, applyng (4) and (5), we have (5) Fg. 4. Dfferental hologram contanng the 3D nformaton of the changes only. (a) Numercally propagated to the ntal knght plane, (b) to the kng plane (now absent), and (c) to the fnal kng plane.

4 to come nto focus somewhere wthn the propagaton range of to mm. Of course, these relatonshps are non-lnear and a numercal smulaton of our constructed system produces a translaton from object space DFOI nto fnal holographc propagaton space as plotted n Fg. 5. Specfcally, our three object postons of nterest consstng of the 425 mm ntal knght poston, the 401 mm kng poston, and the 363 mm fnal knght poston are predcted to be n focus at propagaton dstances; -11.7, -16.3, and mm, respectvely. These three predcted propagaton planes were chosen for dsplay n Fg. 3 and Fg. 4. Clearly, these are approprate planes for the objects n queston. C. Mcroscopc Dfferental Incoherent Holography We have fabrcated a smlar system to that above (Fg. 1) whch we mount drectly to the camera port of a standard commercal mcroscope. In essence, the nput lens s replaced by the mcroscope as the nput devce to create the ntermedate mage space. In ths way, the brght-feld mcroscope mages are successfully recorded here as complex holograms contanng the 3D volumetrc nformaton of the object space extendng above and below the mcroscope s normal nput plane. A slde contanng a USAF1951 resoluton target was placed on the mcroscope stage whle a coverslp contanng two partcle-lke structures was held approxmately 8 mm above by a separate translaton stage. The volume space was llumnated by a sngle color ncoherent LED and an ntal hologram was recorded. The two-partcle system was then translated laterally and a fnal hologram was recorded. Just as above, a dfference hologram was calculated resultng n a hologram contanng only the two-partcle system n ts ntal and fnal postons whle all unchanged nformaton from all planes n the space s absent. A summary of ths experment appears n Fg. 6. Fg. 6(a-c) shows the ampltude representaton of the ntal, fnal, and dfference holograms, respectvely, all propagated to the resoluton target plane. It s obvous n the dfference hologram that ths plane s now devod of the resoluton target nformaton and that only the out-of-focus projectons of the translated two-partcle system are present. Meanwhle, Fg. 6(d-f) contan these same three ampltude holograms, but now propagated to the partcle plane. At ths plane, the two-partcle system s clearly dentfed, n-focus, n the dfference hologram at both ts ntal and fnal postons even though the Fg. 6. Numercal smulaton showng the holographc propagaton dstances, z h, expected for object planes wthn the DFOI. Fg. 5. Summary of dfferental ncoherent holographc mcroscopy experment. (a), (b), and (c) are the ntal, fnal, and dfferental holograms, respectvely, all propagated to the resoluton target plane. (d), (e), and (f) are the ntal, fnal, and dfferental holograms propagated to the partcle plane. (g), (h), and () are the magnary component mages of the ntal, fnal, and dfferental holograms at the partcle plane showng a relatve shft (to whte) n the profle representng the fnal partcle postons. lower partcle was partally obstructed by the resoluton target. We pont out here; nformaton to decpher the ntal and fnal postons of moved objects s preserved n the complex dfference hologram, although ths s hdden n an ampltude representaton. In ths case, we dsplay n Fg. 6(g-) only the magnary component of each of these same holograms and propagate them once agan to the partcle plane. In ths representaton, t s easy to detect the two partcles, dentfed by crcles for convenence, n ther ntal postons n Fg. 6(g), and ther fnal postons n Fg. 6(h). More mportantly, n the dfference hologram, Fg. 6(), the fnal poston of ths twopartcle system s shfted n ths representaton, clearly dstngushng t from the un-shfted ntal poston. III. DISCUSION AND CONCLUSION We have demonstrated that our SIDH process can brdge the gap between 3D holographc magng and exstng ncoherent magng technologes. We specfcally am to combne our technques wth the versatle functonal magng of fluorescence mcroscopy. In ths way, we wll record 3D fluorescence profles and track florescent tags n lvng organsms wthout the use of phototoxc raster scannng of pont detecton [10]. Addtonally, we am to mprove measurement precson of bologcal cell tracton force prevously measured by quanttatve phase magng of surface wrnkles caused by cellular movement [11]. A deformable gel could be labeled wth fluorescent beads tracked by dfferental fluorescence holography after cellular moton across the substrate as outlned n Fg. 7. We are also currently developng a sngle-shot, off-axs SIDH method whch wll elmnate the need for phase-shftng by ncorporatng a slght tlt between the self-nterferng copes [12]. Ths may be qute sgnfcant for dynamc bologcal applcatons where temporal resoluton s mportant as well as

5 REFERENCES Fg. 7. Deformable stuff lke prevous wrnkles. fluor beads n deformable matrx. DHFM wth mechancal deformaton (how?). crawlng cells cultured on top surface. vastly mproved frame rates for 3D holographc vdeo photography. ACKNOWLEDGMENT We would lke to thank Dr. Byeong Cha from the Department of Molecular Pharmacology & Physology of Unversty of South Florda Morsan College of Medcne for hs helpful nput on bologcal and fluorescence applcatons. [1] Harharan, P., [Optcal Holography: Prncples, Technques, and Applcatons], Cambrdge Unversty, (1996). [2] Gabor, D., A new mcroscopc prncple, Nature 161(4098), (1948). [3] Leth, E. N. and Upatneks, J., Wavefront reconstructon wth contnuous-tone objects, J. Opt. Soc. Am. 53, (1963). [4] Rosen, J. and Brooker, G., Non-scannng motonless fluorescence three-dmensonal holographc mcroscopy, Nat. Photoncs 2, (2008). [5] Rosen, J. and Brooker, G., Fluorescence ncoherent color holography, Opt. Express 15, (2007). [6] Rosen, J. and Brooker, G., Dgtal spatally ncoherent Fresnel holography, Opt. Lett. 32, (2007). [7] Km, M. K., Incoherent dgtal holographc adaptve optcs, Appl. Opt. 52, A117 A130 (2013). [8] Yamaguch, I. and Zhang, T., Phase-shftng dgtal holography, Opt. Lett. 22, (1997). [9] Dubos, F., Callens, N., Yourassowsky, C., Hoyos, M., Kurowsk, P., and Monnom, O., Dgtal holographc mcroscopy wth reduced spatal coherence for three-dmensonal partcle flow analyss, Appl. Opt. 45, (2006). [10] Lorbeer, Raoul-Amadeus, et al., Hghly effcent 3D fluorescence mcroscopy wth a scannng laser optcal tomograph, Opt Express 19, (2011). [11] Yu, Xao, et al., Measurement of the tracton force of bologcal cells by dgtal holography, Bomed Opt Express 3, (2012). [12] Hong, J. and Km, M. K.. Sngle-shot self-nterference ncoherent dgtal holography usng off-axs confguraton, Opt. Lett. 38, (2013).