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Optical simulation experiment for X-ray holography
Vohmw 9, number 3
OPTICS COMMUNICATIONS
November 1973
OPTICAL SIMULATION EXPERIMENT FOR X-RAY HOLOGRAPHY ~ u. RODER, D. GUTKOWICZ-.KRUSIN and H. MAHR Laboraton.: oJ'A tomic and SolM State Physics, Cornell University, Ithaca, New York 14850. USA Received 26 September 1973
t:qng a l-resnel zone plate to obtain a reference point source as well as object illumination a hologram was produced with quasi-thermal light. This experiment is a scaled up simulation of a proposed experiment to produce saft X-ray holo~ams. An intensive search over file last few years for sources showing stimulated emission in the far l..A: and soft X-ray tenon has renewed interest in holography at these wavelengths, it was first suggested by Winthrop and Worthington [ 1] that the lensless Fourier-trans. form type holography would be suitable for X-rays. Their optical analog experiment demonstrated the appiicability o f that m e t h o d 12]. More recently' one-dimensional holograms of this type were recorded by Kik:.ta eta]. [3] with carbon Ka radiation, and by Aoki et al. [41 with synchrotron radiation. In both ,a,es. d:c recop, slrt~clion was made using laser radia.'.>,>. :p, ,.he visible region. tn order to extend their method to two- or threed6w.ensiona} objects, it is necessaD' to replace a one. dimensional reference source by a point source. The si:e of this source should be determined by optimizing ~wo opposing conditions. The diameter of the pinhole should be as !arge as possible to maximize the intensity o f ',he reference beam. On the other hand, the resolu,.ion condition requires a reference source of small size. One way to t~ercome this difficulty', as suggested by Smoke [51 is the resolution retrieving compensation. i lowever, with presently available X-ray sources, it is d,~bt r-t~lwhether the coherepce requirements would N., tulfi!led. In this paper, a different method is con-
sidered, in which conditions o f sufficiently high intensity in the reference beam and of the small size of the source are both fulfilled. The method is suited for presently available incoherent as well as future coherent (laser) X-ray sources. This letter reports the results o f ~ul optical analog experiment. An experiment using Be K,~ X-radiation is in progress. The basic element of our experimental arrangement is a Fresnel zone plate which is used as a beam splitter as well as a focusing lens for the reference beam. The dominant terms in the intensity distributioll of radiation passing dtrough the zone plate are the zeroth and two first orders: the intensity of other orders ate dependent on the transmission function o f the zone plate and are negligible, in our setup the zone plate, consisting o f alternating opaque and transparent zones, is coherently iUuminated by a pointlike source. The image of the source due to the convergent first order is used as a point reference source. An object transparency placed next to this reference point is illuminated essentially by the directly transtnitted zeroth order with small contributions from the diverging first order. So, loosely speaking, one can think of the Fresnel zone plate in this setup as being a lens with a hole drilled through the center. The focal length o f a Fresnel zone plate is given by f = r f / ^ , where r 1 is the radius of the inner disk ~md ~, the wavelength of the radiation. The smallest comtnercially available zone plate that we could locate is made by Buckbee Mears Co. and consists of 19 clear and lq solid rings made o f a 0.0005 inch thick gold foil. The 2'
~ ~,~,~rk,;upp~rted in part by the U.S. Office of Naval Research u~dcr contract N00D14-67-A-0077-00l 9, Technical Report =t 8, and by /he National Science Foundation under Grant ---G}1-336_~,7thrt~ugh the Malerials Science Center al ('ornell UniversiLv. MSC Repo;t =2088. 270
.
Volume 9, number 3
OPTICS COMMUNICATIONS
November 1973
this radiation f = 23 cm. To test the idea an optical analog e,xperiment was performed in which f was kept constaut and a photographically enlarged copy of the zone l~late, with a clear central disk, was made such that r~/X = constant. Intended for X = 5145 A a 7-fold magnification of the zone plate was recorded on an Agfa 10E56 photo plate (fig. la). This magnification scales the size of the zone plate from the intended X-ray experiment to the light experiment by the square root o f the ratio of tile two wavelengths. The experimental set-up is given in fig. 2. The beam of a 1 W argon ion laser was focussed, with a microscope objective, on a rotating disk of ground glass in order to obtain a high intensity quasithermal pointlike source. The Fresnel zone plate, separated by a distance of 2 f f r o m th,e ground glass disk, was illuminated by radiation within the coherence angle of this source. An opaque mask was placed at a distance of 2 f from the zone plate. It contained a 5 0 # diameter pinhole to pass the focussed reference beam and a transparent letter Z as an object lo~ated about 750/a from the pinhole. This mask was made by photographic reduction from an original made with black Zip-a-Tone (fig. l b). The reference pinhole was aligned with the image of the source, The holographic information was sampled at another distance 2 / f r o m the object mask. This distance was sufficient to get a complete overlap of the reference and object fields. The resulting lensless Fourier-transform hologram had a fringc spacing of approximately 0.25 ram. Instead. of recording the hologram directly at this point an additional lens system was employed (called field lens and
Ni°
Fig. I. a. A photograph of the Fresnel zone plate, b. A reproduction of the mask used in the object plane. inner disk diameter is 102 #, To avoid overly tong distances with the given zone plate an experinaent with Be K,x (~, = 114A) X-radiation was contemplated: for
object
ratoting
ground gloss
loser ~ - - - ~ ~-.~ - J I" " ~ microscope objective
zone / plate//~
|
mask
\
| i
\
~
|
..J" \ ~
"~
-
T|
-'~.
I |
/ '
\reference
pinhole
hologram plane
V
0
micr. obj
field lens
photo plate
I:ig. 2. Schematic uf the experimentM setup. 271
Volume t/, numlv,'r 3
OPTICS COMMUNICATIONS
November 1973
Fig. 3. A reproduction of the hologram (about 150 u diameter).
microscope objective in fig. 2) to reduce the dimen~ons of the hologram by a factor 50. This final holo~aphic image was recorded on Agfa 10E56 plates ffig. 3 ~. Yhe last step of reducing the size of the hologram served as part o f the simulation of the proposed X-ray experiment. A hologram taken with Be Kc~ radiation (,~ = 114 A) and the original zone plate would have this size (reduced by the ratio of the light to the X-,ay ~avelengths). The use of 5145 A radiation in the reconstruction process will then magnify the object about 50-fold just as it would for a real X-ray hologram. In the reconstruction process the required pointlike source was provided by a spatial filter placed in the ar. gon ion laser beana at a dist~ce of 2 f from the holo~am. A lens behind the hologram converted the reconstructued virtual images into real ones. The real images were recorded (fig. 4). As shown there is sufficient separation between the first and zero orders. The problem of simultaneous recording of high and low frequencies of t.he object spectrum is a characteristic feature of the Fouder-:ransform holegraphy. As one can see in fig. 3, 7 ~
~
,.¥y.:
.~f '
,.; *4
Fig. 4. The reconstructed object. the inner part of the hologram is slightly overexposed, so that information on low frequencies is lost. Present-
Volume 9, number 3
OPTICS COMMUNICATIONS
ly known methods [6] of improvement do not seem to be appLicable for :~-ray holography. Another problent is the fact that the illumination of the object is not homogeneous over its area. In order to have more uniform illumination of the object, we suggest to keep only the outer bands of the Fresnei zone plate thus leaving a sufficiently large transparent inner zone for the object illumination. Inherent in this method is a nonuniform intensity distribution of the reference beam in the hologram plane as the first order shows some diffraction pattern. Therefore the use of a pointlike reconstruction source with uniform intensity at the hologram plane will result in some structure inside the reconstructed object. The above experiment has clearly demonstrated the possibility to record a hologram of a two- or three-dimensional object in the soft X-ray region with presently available equipment. The use of a Fresnel zone plate as a beam splitter allows to avoid the rather stringent overlap conditions encountered in previous experiments [3.4] since the divergence of the focussed reference beam can exceed the one caused by diffraction at object and reference transparencies. Moreover, the higher intensity of the reference beana makes the recording of holograms of two- or three-dimensional objects possible. A difficulty of this method lies in obtaining a uniform ilhmfination of the object, but this may
November 1973
be improved by removing one or two opaqu.e inner bands of the zone plate, without a drastic deterioration t~f the intensity and shape of the first order in its focal plane [7]. A major advantage of this method is its applicability for X-rays of shorter wavelengths, provided a zone plate of smaller size can be produced, With a zone plate 5 times smaller in diameter this experimentaI setup could be used without any changes in distances between elements for a recording wavelength of 5 A.
References l 11 J.T. Winthrop and C.R. Worthington, Phys. Letters 15 (1965) 124. [2] J.T. Winthrop and C.R. Worthington, Phys. Letters 21 (1966)413. [3J S. Kikuta, S. Aoki, S. Kosaki and K. Kohra, Opt. Comm. 5 11972) 86. [41 S. Aoki, Y. lchihara and S. Kikuta, Japan J. Appl. Phys. ll (1972) 1857. JSJ G.W. Stroke, R. Restrick, A. Vunkhouser and D. Brumm, Phys. Letters 18 (1965) 274. [6] For example, R.J. Collier, C.B. Burckhardt and L.It. Lin, Optical Holography (Academic, New York, 19711. 17J P.N Kcating, R.K. Mueller and T. Sawatari, J. Opt. Soc. Am. 62 11972) 945.
273
OPTICS COMMUNICATIONS
November 1973
OPTICAL SIMULATION EXPERIMENT FOR X-RAY HOLOGRAPHY ~ u. RODER, D. GUTKOWICZ-.KRUSIN and H. MAHR Laboraton.: oJ'A tomic and SolM State Physics, Cornell University, Ithaca, New York 14850. USA Received 26 September 1973
t:qng a l-resnel zone plate to obtain a reference point source as well as object illumination a hologram was produced with quasi-thermal light. This experiment is a scaled up simulation of a proposed experiment to produce saft X-ray holo~ams. An intensive search over file last few years for sources showing stimulated emission in the far l..A: and soft X-ray tenon has renewed interest in holography at these wavelengths, it was first suggested by Winthrop and Worthington [ 1] that the lensless Fourier-trans. form type holography would be suitable for X-rays. Their optical analog experiment demonstrated the appiicability o f that m e t h o d 12]. More recently' one-dimensional holograms of this type were recorded by Kik:.ta eta]. [3] with carbon Ka radiation, and by Aoki et al. [41 with synchrotron radiation. In both ,a,es. d:c recop, slrt~clion was made using laser radia.'.>,>. :p, ,.he visible region. tn order to extend their method to two- or threed6w.ensiona} objects, it is necessaD' to replace a one. dimensional reference source by a point source. The si:e of this source should be determined by optimizing ~wo opposing conditions. The diameter of the pinhole should be as !arge as possible to maximize the intensity o f ',he reference beam. On the other hand, the resolu,.ion condition requires a reference source of small size. One way to t~ercome this difficulty', as suggested by Smoke [51 is the resolution retrieving compensation. i lowever, with presently available X-ray sources, it is d,~bt r-t~lwhether the coherepce requirements would N., tulfi!led. In this paper, a different method is con-
sidered, in which conditions o f sufficiently high intensity in the reference beam and of the small size of the source are both fulfilled. The method is suited for presently available incoherent as well as future coherent (laser) X-ray sources. This letter reports the results o f ~ul optical analog experiment. An experiment using Be K,~ X-radiation is in progress. The basic element of our experimental arrangement is a Fresnel zone plate which is used as a beam splitter as well as a focusing lens for the reference beam. The dominant terms in the intensity distributioll of radiation passing dtrough the zone plate are the zeroth and two first orders: the intensity of other orders ate dependent on the transmission function o f the zone plate and are negligible, in our setup the zone plate, consisting o f alternating opaque and transparent zones, is coherently iUuminated by a pointlike source. The image of the source due to the convergent first order is used as a point reference source. An object transparency placed next to this reference point is illuminated essentially by the directly transtnitted zeroth order with small contributions from the diverging first order. So, loosely speaking, one can think of the Fresnel zone plate in this setup as being a lens with a hole drilled through the center. The focal length o f a Fresnel zone plate is given by f = r f / ^ , where r 1 is the radius of the inner disk ~md ~, the wavelength of the radiation. The smallest comtnercially available zone plate that we could locate is made by Buckbee Mears Co. and consists of 19 clear and lq solid rings made o f a 0.0005 inch thick gold foil. The 2'
~ ~,~,~rk,;upp~rted in part by the U.S. Office of Naval Research u~dcr contract N00D14-67-A-0077-00l 9, Technical Report =t 8, and by /he National Science Foundation under Grant ---G}1-336_~,7thrt~ugh the Malerials Science Center al ('ornell UniversiLv. MSC Repo;t =2088. 270
.
Volume 9, number 3
OPTICS COMMUNICATIONS
November 1973
this radiation f = 23 cm. To test the idea an optical analog e,xperiment was performed in which f was kept constaut and a photographically enlarged copy of the zone l~late, with a clear central disk, was made such that r~/X = constant. Intended for X = 5145 A a 7-fold magnification of the zone plate was recorded on an Agfa 10E56 photo plate (fig. la). This magnification scales the size of the zone plate from the intended X-ray experiment to the light experiment by the square root o f the ratio of tile two wavelengths. The experimental set-up is given in fig. 2. The beam of a 1 W argon ion laser was focussed, with a microscope objective, on a rotating disk of ground glass in order to obtain a high intensity quasithermal pointlike source. The Fresnel zone plate, separated by a distance of 2 f f r o m th,e ground glass disk, was illuminated by radiation within the coherence angle of this source. An opaque mask was placed at a distance of 2 f from the zone plate. It contained a 5 0 # diameter pinhole to pass the focussed reference beam and a transparent letter Z as an object lo~ated about 750/a from the pinhole. This mask was made by photographic reduction from an original made with black Zip-a-Tone (fig. l b). The reference pinhole was aligned with the image of the source, The holographic information was sampled at another distance 2 / f r o m the object mask. This distance was sufficient to get a complete overlap of the reference and object fields. The resulting lensless Fourier-transform hologram had a fringc spacing of approximately 0.25 ram. Instead. of recording the hologram directly at this point an additional lens system was employed (called field lens and
Ni°
Fig. I. a. A photograph of the Fresnel zone plate, b. A reproduction of the mask used in the object plane. inner disk diameter is 102 #, To avoid overly tong distances with the given zone plate an experinaent with Be K,x (~, = 114A) X-radiation was contemplated: for
object
ratoting
ground gloss
loser ~ - - - ~ ~-.~ - J I" " ~ microscope objective
zone / plate//~
|
mask
\
| i
\
~
|
..J" \ ~
"~
-
T|
-'~.
I |
/ '
\reference
pinhole
hologram plane
V
0
micr. obj
field lens
photo plate
I:ig. 2. Schematic uf the experimentM setup. 271
Volume t/, numlv,'r 3
OPTICS COMMUNICATIONS
November 1973
Fig. 3. A reproduction of the hologram (about 150 u diameter).
microscope objective in fig. 2) to reduce the dimen~ons of the hologram by a factor 50. This final holo~aphic image was recorded on Agfa 10E56 plates ffig. 3 ~. Yhe last step of reducing the size of the hologram served as part o f the simulation of the proposed X-ray experiment. A hologram taken with Be Kc~ radiation (,~ = 114 A) and the original zone plate would have this size (reduced by the ratio of the light to the X-,ay ~avelengths). The use of 5145 A radiation in the reconstruction process will then magnify the object about 50-fold just as it would for a real X-ray hologram. In the reconstruction process the required pointlike source was provided by a spatial filter placed in the ar. gon ion laser beana at a dist~ce of 2 f from the holo~am. A lens behind the hologram converted the reconstructued virtual images into real ones. The real images were recorded (fig. 4). As shown there is sufficient separation between the first and zero orders. The problem of simultaneous recording of high and low frequencies of t.he object spectrum is a characteristic feature of the Fouder-:ransform holegraphy. As one can see in fig. 3, 7 ~
~
,.¥y.:
.~f '
,.; *4
Fig. 4. The reconstructed object. the inner part of the hologram is slightly overexposed, so that information on low frequencies is lost. Present-
Volume 9, number 3
OPTICS COMMUNICATIONS
ly known methods [6] of improvement do not seem to be appLicable for :~-ray holography. Another problent is the fact that the illumination of the object is not homogeneous over its area. In order to have more uniform illumination of the object, we suggest to keep only the outer bands of the Fresnei zone plate thus leaving a sufficiently large transparent inner zone for the object illumination. Inherent in this method is a nonuniform intensity distribution of the reference beam in the hologram plane as the first order shows some diffraction pattern. Therefore the use of a pointlike reconstruction source with uniform intensity at the hologram plane will result in some structure inside the reconstructed object. The above experiment has clearly demonstrated the possibility to record a hologram of a two- or three-dimensional object in the soft X-ray region with presently available equipment. The use of a Fresnel zone plate as a beam splitter allows to avoid the rather stringent overlap conditions encountered in previous experiments [3.4] since the divergence of the focussed reference beam can exceed the one caused by diffraction at object and reference transparencies. Moreover, the higher intensity of the reference beana makes the recording of holograms of two- or three-dimensional objects possible. A difficulty of this method lies in obtaining a uniform ilhmfination of the object, but this may
November 1973
be improved by removing one or two opaqu.e inner bands of the zone plate, without a drastic deterioration t~f the intensity and shape of the first order in its focal plane [7]. A major advantage of this method is its applicability for X-rays of shorter wavelengths, provided a zone plate of smaller size can be produced, With a zone plate 5 times smaller in diameter this experimentaI setup could be used without any changes in distances between elements for a recording wavelength of 5 A.
References l 11 J.T. Winthrop and C.R. Worthington, Phys. Letters 15 (1965) 124. [2] J.T. Winthrop and C.R. Worthington, Phys. Letters 21 (1966)413. [3J S. Kikuta, S. Aoki, S. Kosaki and K. Kohra, Opt. Comm. 5 11972) 86. [41 S. Aoki, Y. lchihara and S. Kikuta, Japan J. Appl. Phys. ll (1972) 1857. JSJ G.W. Stroke, R. Restrick, A. Vunkhouser and D. Brumm, Phys. Letters 18 (1965) 274. [6] For example, R.J. Collier, C.B. Burckhardt and L.It. Lin, Optical Holography (Academic, New York, 19711. 17J P.N Kcating, R.K. Mueller and T. Sawatari, J. Opt. Soc. Am. 62 11972) 945.
273