holographic deblur of photos ceas--188

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Volume 1, number 3 OPTICS COMMUNICATIONS July/August 1969

D EB LU R R IN G O F MO TIO N -B LU R R ED PH O TO G R A PH SUSING EXTE NDED-RA NGE HOL OGRAPH IC FOURIE R-TRANS FORM DIVISION

George W. STROKE, Franz FURRER * and Donald R. LAMBERTY **Electro-Optical Sciences Center, State University of New York,Stony Brook, New York 11790, USA

Received 2 June 1969

The method of a poster iori image-correcting deconvolution by holographic Fourier -tran sfor m division(Stroke and Zech, Phy sic s Let ter s 25A (1967) 89) has been successfully extended to the deblur ring ofphotographs b lur red by motion with the aid of a photographic (positive + negative) nmaskingn process,used to obtain the required great line ar dynamic range (especially in the Fourier- trans form domain), inanticipation of extended-range high-resolution fil ms now under development.

There has ari sen an increasing interest inmethods which permit one to extrac t a posterioria sharpened image from a photograph blurred asa r esult of various instrumental and recordingimperfections, including blurr ing by atmospher icturbulence and indeed by motion. In a gene ralway optical image deblurring methods are basedon the principles of 'spatial filtering' describedby Mar6chal and Croce [I]. Considerable succes sin implementing these principles were demon-strated already a decade ago by Tsujiuchi [2]who showed that the required complex (amplitudeand phase) filt ers [3] could be realized by a com-bination of two fil ters: the amplitude fil ter ,realized by photography, and the phase filter ,rea lized by vacuum evaporation. The Tsujiuchimethod is particularly suitable for the prepara-tion of f ilt ers which may be described in analyti-cal form. It has been used, for instance, to de-blurr images blurred by artifi cial (laboratory)turbulence and indeed for certain types of motion[4]. Several other image-deblurring methodshave also been demonstrated, including digital-computer implementation of the required Fourier-trans form division [5] a s well as purely elec-tronic methods, particular ly suitable in conjunc-tion with television devices [6,7]. The relativemer its of these and other methods ar e formingthe subject of cu rrent investigations by a numberof authors. Somewhat in analogy with the res ul tsof the investigations of Jacquinot and Chabbal,with regard to relative mer its of various formsof spectroscopy, it is probable that each of theimage-deblurring methods may be particularlysuitable fo r some types of applications, while not

necessarily being the most powerful generalmethod. However, in keeping with the suggestionby Stroke and Zech [8] it has become increasing-ly apparent that the most general method for op-tical image deblurring will no doubt be mostreadily implemented by holographic means. Thegeneral background for the holographic imagedeblurring methods may be found in refs. [8-111,in which we also discuss the difference betweenthe holographic image resto ration methods (solu-tion of an integral equation) on the one hand, and,on the other, the correla tive character recogni-tion methods [12] Vormation of an integral equa-tion). In addition to the methods of refs. [8-111,which use a holographically synthesized filt er forthe purpose of solving the integral equation (con-volution integral) by division in the spatial Four-ier -tra nsform domain, Stroke [13,14] has alsoproposed a different type of holographic methodwhich permi ts one to achieve 'image-deblurring'a s well as 'aper ture synthesis' simply by takinga hologram of the blurred photograph and by il -luminating it with the light from the sp read func-tion h(x ,y) , in one of the arrangements. Thesemethods [13,14] a re particularly suitable for thecase when the auto-correlation function of thespread function is sharply peaked. Detailedcomparison of the various holographic methodsa re given in ref. [15]. It may be of interest tofurther note that spatial Fourier-transform divi-* Visiting staff, from th e Photographisches Institut(Director, Pro fessor Dr. W. F. Berg), Eidgen6s-sische Techn ische Hochschule, Zurich.** Visiting staff, from the CBS Laboratories, Stam-ford, Connecticut.


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Volume 1, number 3 OPTICS COMMUNICATIONS July/August 1 9 6 9

Fig. 1 .a) Photograph of 4 x 4 mm test chart, deliberately blur red by motion of the 240 mm Schneider Symmar lens(f/5.6) used in the recordi ng of the photograph in white light (zir conium arc ). The dimensi ons of the blur red photo-graph a re 10 % 10 mm. The lens was deliberately moved by hand with the aid of a micr ome ter and ball-slide arran ge-ment. The type of motion can be evaluated by looking at the "sp rea d function" h(x, y) indicated by the small verticalarrow . It can also be seen by the "doubling" of th e numerals (for instance that indicated by the slanted arr ow) , show-ing that the motion was in fact not linear with tim e.b) Holographically deblu rre d photograph, using method of S troke and Zech [8]with "extended-range" fil ter a s de-scribed in text. The clearly apparent considerable degre e of 'deblurring' may be evaluated by noting that the spre adfunction of fig. l a has been reduced almost to a point (indicated by vertical arrow), and als o that the "doubled" nume-ra ls , which had almos t equal intensity in fig. la , have been rest ore d to a single numeral. It is important to notethat restoration of a single image fr om such ndoubledn motion-blurred photographs, a s achieved holographicallyhe re , could not possibly be achieved by the well-known purel y photographic 'masking' and printing methods, a s usedin reproduction, among other applications. It is also important to note that nothing mo re than the s pread functionh(x,y) (fig. la ) was requir ed to synthesize the image-deblurring deconvolution fil ter (see fig. 2).

sion f ilte rs may in some instances be generatedin binary fo rm by computer: a s shown by Loh-mann and Paris [16], it is necessary for thispurpo se to have some way of f i rs t obtaining ananalytical expression for the required filter. Inthe methods which we discuss here, the requiredFourier-transform division filter is directlygenerated by an analogue optical method [8]starting fr om the spread function h(x,y) (seefigs. 1 and 2) .

Before giving the experimental details for theres ult s shown in figs. 1 and 2, we give the theor -etic al principles of o ur method [8] a s it applies

where h(x ,y), the spr ead function, is the blurredimage of a single point in the object domain.Within the band limits, discussed in ref. [15],eq . (1)may be written in the spatial Fouriertransform domain [3 ] in the form

G = F H . (2)Within the same lim itations, we may extract thefunction FBL rom G by Fourier-transform divi-sion, in the for m

to this work. Let g(x,y) d esc ribe -the exposure E FB L = G/H G -1 .[proportional to the intensity distribution I ( x ,y)] (3)in the original blurred photograph. Let f(x, y) be The symbol FBL s used to indicate the well-th e image which would be formed by the given known fact that no d irec t ima ge-restora tionoptical inst rument in the absence of image-de- method is capable of rest oring those spatial fre -grading blurring. We re ca ll that f (x, y) may be quencies in F which have been degraded to zeroconsidered a s he "diffraction limitedn image in the original image-recording (i.e. photography)which would be formed by the given instrument process. Nevertheless, extensive experienceif it had no aberrations or other blurring imp er- has now shown without any doubt that image-fections, notably motion, which we consider rest orat ion methods, such a s that which we de-her e. The blurr ed photograph may therefore be scribe, result in a considerable visual improve-desc ribed by the equation ment of a blu rre d imag e (see e.g. fig. I) , even


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Volume 1,number 3 OPTICS COMiI'IUNICATIQNS July/August 1969

Fig. 2. Positi ve print of Fouri er-trans form division fil ter component HI-^ used in the holographic deblurring shownin fig. 1, ogether with density step-wedge used to obtain the fil ter ov er an "extended" dynamic range, as describedin text. The arr ow indicated the orientation of the fil ter re lative to the direction of blurring motion (filter parallel tomotion). The sca le of the filt er a s used with 2 300 m m focal length Fourier-transforming lenses is indicated by thelcm mark.

though the information content will, in general,be probably even slightly degraded in the rest oredimage, a s compared to the blur red image. Theparadoxical nature of thi s fact may be explainedby the observation that the human observer iscapable of more readily recognizing and in ter -preting images in a "restoredw orm than intheir original "blurredw form.

The Fourier-transform division filter H-lrequired t o perform the division in eq. (3) maybe rea liz ed in the form of a two-component" andwichn

H-l= H * / ( H ~ % ( 4 )a s fi rs t proposed by Stroke and Zech [8], wherewe rec all that H(u, v) is r elated to the spreadfunction h(x, y ) by the spatial Fourier transfor-mation

H(u,v) = J ~ ( x , Y ) xp [27ii(ux +vy)]dxdy (5)given in normalized form [3], with simi lar equa-tion s holding for G(u, v) and F(u , v) in relat ion togk,y ) and f (x,y). The H* part of the fil ter i s a

2Fourier- transform hologram, and the 1 H partis a photograph of H, developed with a photo-graphic "gamman equal to 2 (see refs . [3,8-11,,15]).It is a solution to the crucially important (andhere tofore very difficult) problem of obtaining therecordin g of lH1 over the requ ired lar ge ex-posure range with a linear c urve of slope equalto 2, which we wish to briefly report here. It i simportant to recognize that intensity ranges inthe spatial frequency (Fourier-transform) do-main will in general be considerably la rge r thanin the spatial (photographic transparency) do-main. Fo r instance, in one case, we found, inagreemen t with theoretica l prediction, that atest chart with spatial frequencies up to 40 lines/mm had an intensity range in the Fouri er-t rans -fo rm domain in exce ss of l o 4 i.e. logE in excessof 4.0. Normally processed 14C70 AGFA-GEVAERT film, which we use in our holographicwork, only permit s one to cover an exposurera nge of just about 1.0 with a gamma of 2, r atherthan the range of 3.0 which we require.It has been clear to one of us (GWS)or quitesom e time that a solution to this problem would


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Volume 1, number 3 OPTICS COMMUNICATIONS July/August 1969cons ist in obtaining certa in types of specialphotographic emuslions, with "extended dynamicrangew of a type not available. Thanks to a mostkind suggestion of Pro fessor Dr. W. F. Berg,and following fur the r suggestions by ProfessorDr. E.Klein and Dr. E.Moisar, of AGFA-GEVAERT [17], it appears that such 'extendeddynamic range' film, suitable for holographicimage processing, is indeed theoretically achiev-able and may soon be available for experimentalpurposes. In the meantime, however, it appearedimportant to us to verify that a considerable im-provement in our holographic image-deblurringmethods would indeed resul t from the u se of amethod which in effect would provide the re-quired maximum possible dynamic range. Theexperience of one of us (FF) with photographic"maskingn methods [18] has proven to give usthe desire d solution, following a kind initiativeof Pro fes sor Dr. W. F. Berg to this effect. Thetheory and principles of the photographic mask-ing process a r e well-lmown [18] and we do notpropose to discuss them further here. However,it may be of in terest , a s an example, to give anoutline of the steps used to obtain the 1 HI -2filter by this means. As a firs t step, by suitablechoice of emulsion, developer, developing timeand temperature, we determine that we canrecord over an exposure range logE = 3. Thenwe proceed as follows:

1. Place log E = 3 density f ilte r in front of H-recording plate.2. Expose test exposures of H on 14C70 fi lmuntil peak of 1H is just observable above thefog. In our case, exposure time x = 400 seconds,developer D76, developing time 1.5 minutes,temperature 75OF.3. In a n enlarger, using Wratten 25A red f i l -ter, place logE = 3 density filter in front of un-exposed 14C70 film.4. Adjust enlarger brightness until x = 400seconds is just recorded through the logE = 3filter.5. Remove log E = 3 filter from in front of H.6. Record H fo r x = 400 seconds on negativeN1-7. On same negative N1 expose by contact inthe enla rger a step wedge for x = 400 seconds(using the Wratten 25A fil ter ). The resul t ofsteps 6 and 7 appear a s in fig. 2.

8. Develop negative N1 a s in 2. Fix, wash,dry9A. Contact print N1 in white light on 14C70film, and develop @exreloper: D76,l: 1, 6 min-utes, 75OF). This is printB. Make "unsharp mask" print on 14C70

film of P ~ , M n white light using a sheet of plas-ti c cliffusor between Pi -M and film. This is mask-ing negative N ~ - Mdeveloper: D76,l: 1, 1 minute,75'~).C. Copy N1-M on 14C70 fi lm in white light.This is positive PI. (developer: D76, normallyconcentrated, 6 minutes, 68OF).10. Contact pr int N1 in white light on 14C70film @76, normally concentrated, 6 minutes,75'~). This is print Pa.

11. Draw graph D - logE for P I +Pa usingred filter in sensitometer), in collimated (paral-lel) light.12. If graph of 11 is not a straight line, re-peat step 9 or step 10 or both until P i +P 2 give astraight-line D - logE curve.13. Now make contact print of P i +P2 on10E70 AGFA-GEVAERT plate. (D76, normallyconcentrated, 3 minutes, 68 '~ ).Step 13 gives a negative N2 having (undersuccessful conditions) the desired gamma equalto 2 over a density range a s large as possible.In our ca se the range extended over a density of40ogE =2). A positive print of N2 (as used in ourexperiments to obtain the deblurring of fig. 1) isshown in fig. 2. This i s the I I -2 filt er compo-nent of our H*/ ( H filter.We also used a comparable masking methodto obtain the J N J ~2 transmittances for g(x,y)and h(x,y) according to refs . [8,10,11]. More ex-tensive details will be given in a future publica-tion [19].We wish to acknowledge the generous supportof the National Aeronautics and Space Administra-tion (Grant NGR-33-015-068-090), the NationalScience Foundation, and the Office of Naval Re-search for the pursuit of th is work. We alsowish to part icularly acknowledge most fruitfulconversations with Professors D. Gabor, W. F.Berg, E. Klein and H. Nassenstein, and with Dr.E.Moisar.

REFERENCES111 A-MarBchal and P.Croce, Compt. Rend. Acad. Sci.(Paris) 23 7 (1953) 607.[2] J.Tsujiuchi, in: Progress in Optics, Vol. 2, ed.E . Wolf (North-Holland, Amsterdam, 1963) p. 133.[3] G. W. Stroke, An introduction to coherent optics

and holography, 2nd ed. (Academic press, ' ~ e wYork, 1969).[4] J . L.Horner, J. Opt. Soc. Am. 59 (1969) 553,558.[5] J.L.Harris, J. Opt. Soc. Am. 56 (1966) 569.[6] P. C . Goldmark and J. M. Hollywood, Proc. IR E 39(1951) 1314.


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Volume 1, number 3 OPTICS COMMUNICATIONS[7] R. .McMann and A.A.Goldberg, J.. Soc. Motion [14] G. w.Strok e, Phys. L et te rs 28A (1968) 252.Pic tu re Television' Engrs . 77 (1968) 22. [15] G. W.Stroke, P ~ o c . f 1968 Floren ce ICO sympo-[8] G. W.Stroke and R.G.Zec h, Phys. L ett er s 25A sium, to app ear in Opt. Acta.

(1967) 89. [I61 A. W. Lohmann and D.P . P a ri s , ~ p p i . pt . 7 (1968)[9] A. W. Lohmann and H. W.Werlich, Phys. Let ter s 651.25A (1967) 570. [17] E.Klein, E Moisar and H. Nassenstein, priva te[lo ] G. W. Strok e, G.Indebetouw and C. Puech, Phys. communication.Let te rs 26A (1968) 443. 1181 C. E.K. Mees and T. . ame s, The theory of the[11] G. W. Strok e, Ph ot. Ko rr . 104 (1968) 82. photographic pro ce ss, 3rd ed. (Macmillan, New

[12] A. Vande r Lugt, IEEE Tra ns. Inform. Theory 10 York, 1966).(1964) 139. [19] W. F-Berg, G.W. Stroke, D.R. Lamberty and F.[I s] G. W. Stroke, Phys. Le tte rs 27A (1968) 405. Furrer, Opt. Acta, in preparation.

holographic deblur of photos ceas--188

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