Hologram coherence effects

Some Effects of Spatial and Temporal Coherence on In-line Fraunhofer Holography

“…If equations (12) It is apparent that the effective size of the hologram becomes small according as the area of spatial coherence decreases, i .e . ro becomes large [2], and it becomes almost constant for large z. Some experiments with respect to this problem will be shown in § 5 .…”

“…For simplicity, a completely coherent light is used for reconstruction. By referring to equations (32) and (34), the reconstructed images are obtained as 2 From these two relations, it is apparent that the amplitude of the reconstructed image is given by the convolution integral between the amplitude transmittance of the object fo and Fourier transform y of degree of longitudinal coherence y . By setting fo = 8 -function the point spread amplitude h a (p, q) is obtained as 2 2 ha (p, q) =~~z h 20) f f y ( 0,0 ;x1,yi ; x1 2~~e xp 11Z (px1+qyi)] dx 1 dyl ( 59 ) and the line spread amplitude is given by z ha(p, q) = 1~(~') f y ( 0, q ; x 1 , q ; 2zc ) exp Czpxl] dx l .…”

“…Holography requires light having good spatial and temporal coherence because it is basically an interference process . From spatial coherence theory, this type of holography was studied by Reynolds and DeVelis [2] but their treatment was in reality troublesome to evaluate the image performance of in-line Fraunhofer holography. We intend to formulate it in a simple way by using a method of stationary phase [3] and to estimate a relationship between the hologram size and coherence property of the illuminating light .…”

“…[4], who studied Fourier transform holography from spatial coherence theory and Fujiwara et al [5], who discussed the effects of spatial coherence on Fresnel holography and temporal coherence on Fourier transform holography. 2 . Recording process for an in-line Fraunhofer hologram Figure 1 shows an arrangement of recording an in-line Fraunhofer hologram .…”

“…where rZ=1/[(ea-x)2+(')t-y2)+z2] for i=1,2, k = 27r/A, A being the wavelength and z is the normal distance between the object and the hologram planes . Substitution of equation (1) into equation (2) produces I(X' Y) = X2 JJJJ F( 1,'11 i C2, r12) eXp [ik(r1-r2)] del d 7 …”