Abstract

When light-in-flight recording by holography is used two different sorts of apparent distortion of the wavefronts exist. The first distortion is common to all types of ultrafast gating viewing system and like relativistic phenomena it is caused by the limited speed of light used for observation. The second distortion is produced by the holographic process itself and is caused by the limited speed of the light pulse used as a reference beam. By using the second distortion to compensate for the first it is possible to manipulate or eliminate apparent wavefront tilts or distortions so that measurement of the 3-D shape of wavefronts or other objects is facilitated. A reconstruction beam that is the conjugate of the reference beam results in three interesting effects, one of which is the reemission of the recorded pulse.

© 1991 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. N. Denisyuk, D. I. Staselko, R. R. Herke, “On the Effect of the Time and Spatial Coherence of Radiation Source on the Image Produced by a Hologram,” in Proceedings, Applications of Holography, Besancon (July1970).
  2. D. I. Staselko, Y. N. Denisyuk, A. G. Smirnow, “Holographic Recording of the Time-Coherence Pattern of a Wave Train from a Pulsed Laser Source,” Opt. Spectrosc. 26, 41 (1969).
  3. N. Abramson, “Light-in-Flight Recording: High-Speed Holographic Motion Pictures of Ultrafast Phenomena,” Appl. Opt. 22, 215–232 (1983).
    [CrossRef] [PubMed]
  4. N. Abramson, The Making and Evaluation of Holograms (Academic, London, 1981), pp. 28, 110, 144, 197.
  5. N. Abramson, “Light-in-Flight Recording. 2: Compensation for the Limited Speed of the Light Used for Observation,” Appl. Opt. 23, 1481–1492 (1984).
    [CrossRef] [PubMed]
  6. N. Abramson, “Single Pulse Light-in-Flight Recording by Holography,” Appl. Opt. 28, 1834–1841 (1989).
    [CrossRef] [PubMed]
  7. N. Abramson, S. Pettersson, H. Bergstrom, “Light-in-Flight Recording. 5: Theory of Slowing Down the Faster-than-Light Motion of the Light Shutter,” Appl. Opt. 28, 759–765 (1989).
    [CrossRef] [PubMed]
  8. R. K. Kaarli, A. K. Rebane, P. M. Saari, “4-D Holography and Storage of Ultrafast Time-Domain Signals,” in Proceedings, International Conference on Optical Science and Engineering, Paris (Apr.1989).
  9. C. Joubert, M. L. Roblin, R. Grousson, P. Lavallard, “Holographic Method to Realize a Temporal Phase Conjugation Mirror by Inversion of the Spectral Phase of a Picosecond Pulse,” in Proceedings, International Conference on Optical Science and Engineering, Paris (Apr.1989).

1989 (2)

1984 (1)

1983 (1)

1969 (1)

D. I. Staselko, Y. N. Denisyuk, A. G. Smirnow, “Holographic Recording of the Time-Coherence Pattern of a Wave Train from a Pulsed Laser Source,” Opt. Spectrosc. 26, 41 (1969).

Abramson, N.

Bergstrom, H.

Denisyuk, Y. N.

D. I. Staselko, Y. N. Denisyuk, A. G. Smirnow, “Holographic Recording of the Time-Coherence Pattern of a Wave Train from a Pulsed Laser Source,” Opt. Spectrosc. 26, 41 (1969).

Y. N. Denisyuk, D. I. Staselko, R. R. Herke, “On the Effect of the Time and Spatial Coherence of Radiation Source on the Image Produced by a Hologram,” in Proceedings, Applications of Holography, Besancon (July1970).

Grousson, R.

C. Joubert, M. L. Roblin, R. Grousson, P. Lavallard, “Holographic Method to Realize a Temporal Phase Conjugation Mirror by Inversion of the Spectral Phase of a Picosecond Pulse,” in Proceedings, International Conference on Optical Science and Engineering, Paris (Apr.1989).

Herke, R. R.

Y. N. Denisyuk, D. I. Staselko, R. R. Herke, “On the Effect of the Time and Spatial Coherence of Radiation Source on the Image Produced by a Hologram,” in Proceedings, Applications of Holography, Besancon (July1970).

Joubert, C.

C. Joubert, M. L. Roblin, R. Grousson, P. Lavallard, “Holographic Method to Realize a Temporal Phase Conjugation Mirror by Inversion of the Spectral Phase of a Picosecond Pulse,” in Proceedings, International Conference on Optical Science and Engineering, Paris (Apr.1989).

Kaarli, R. K.

R. K. Kaarli, A. K. Rebane, P. M. Saari, “4-D Holography and Storage of Ultrafast Time-Domain Signals,” in Proceedings, International Conference on Optical Science and Engineering, Paris (Apr.1989).

Lavallard, P.

C. Joubert, M. L. Roblin, R. Grousson, P. Lavallard, “Holographic Method to Realize a Temporal Phase Conjugation Mirror by Inversion of the Spectral Phase of a Picosecond Pulse,” in Proceedings, International Conference on Optical Science and Engineering, Paris (Apr.1989).

Pettersson, S.

Rebane, A. K.

R. K. Kaarli, A. K. Rebane, P. M. Saari, “4-D Holography and Storage of Ultrafast Time-Domain Signals,” in Proceedings, International Conference on Optical Science and Engineering, Paris (Apr.1989).

Roblin, M. L.

C. Joubert, M. L. Roblin, R. Grousson, P. Lavallard, “Holographic Method to Realize a Temporal Phase Conjugation Mirror by Inversion of the Spectral Phase of a Picosecond Pulse,” in Proceedings, International Conference on Optical Science and Engineering, Paris (Apr.1989).

Saari, P. M.

R. K. Kaarli, A. K. Rebane, P. M. Saari, “4-D Holography and Storage of Ultrafast Time-Domain Signals,” in Proceedings, International Conference on Optical Science and Engineering, Paris (Apr.1989).

Smirnow, A. G.

D. I. Staselko, Y. N. Denisyuk, A. G. Smirnow, “Holographic Recording of the Time-Coherence Pattern of a Wave Train from a Pulsed Laser Source,” Opt. Spectrosc. 26, 41 (1969).

Staselko, D. I.

D. I. Staselko, Y. N. Denisyuk, A. G. Smirnow, “Holographic Recording of the Time-Coherence Pattern of a Wave Train from a Pulsed Laser Source,” Opt. Spectrosc. 26, 41 (1969).

Y. N. Denisyuk, D. I. Staselko, R. R. Herke, “On the Effect of the Time and Spatial Coherence of Radiation Source on the Image Produced by a Hologram,” in Proceedings, Applications of Holography, Besancon (July1970).

Appl. Opt. (4)

Opt. Spectrosc. (1)

D. I. Staselko, Y. N. Denisyuk, A. G. Smirnow, “Holographic Recording of the Time-Coherence Pattern of a Wave Train from a Pulsed Laser Source,” Opt. Spectrosc. 26, 41 (1969).

Other (4)

Y. N. Denisyuk, D. I. Staselko, R. R. Herke, “On the Effect of the Time and Spatial Coherence of Radiation Source on the Image Produced by a Hologram,” in Proceedings, Applications of Holography, Besancon (July1970).

N. Abramson, The Making and Evaluation of Holograms (Academic, London, 1981), pp. 28, 110, 144, 197.

R. K. Kaarli, A. K. Rebane, P. M. Saari, “4-D Holography and Storage of Ultrafast Time-Domain Signals,” in Proceedings, International Conference on Optical Science and Engineering, Paris (Apr.1989).

C. Joubert, M. L. Roblin, R. Grousson, P. Lavallard, “Holographic Method to Realize a Temporal Phase Conjugation Mirror by Inversion of the Spectral Phase of a Picosecond Pulse,” in Proceedings, International Conference on Optical Science and Engineering, Paris (Apr.1989).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (25)

Fig. 1
Fig. 1

Holodiagram consisting of a set of concentric ellipses representing constant path length for light from A to B. Adjacent ellipses represent a constant difference in path length, which could represent wavelength, coherence length, or pulse length.

Fig. 2
Fig. 2

Separation of the ellipses of the holodiagram varies by a factor k which is constant along arcs of circles through A and B. Thus the apparent values of wavelength, coherence length, and pulse length are found by multiplying the true values by k.

Fig. 3
Fig. 3

Ellipses studied from point B at a distance R behind hologram plate H, which is illuminated by the reference beam from D. In that case the ellipses appear distorted, e.g., from the ellipse of the holodiagram that passes through C to curve FCG. This distortion is caused by the time it takes for the pulse from D to travel along the hologram plate.

Fig. 4
Fig. 4

Equation of an ellipse is usually expressed in a and b. To express the path lengths of Fig. 3 we prefer to use distances L and c.

Fig. 5
Fig. 5

Light source A illuminates a smoke-filled box at C and the pulse front is observed from B behind hologram plate H. Angle ACB is 2α. The true pulse front (P1) is perpendicular to AC, but because of the limited speed of light it appears to be rotated by angle α so that it becomes normal to the bisector of ACB (P2). Because of the holographic process it appears further rotated by angle β to P4. By observing the reconstruction of C from a certain distance R behind H, angle β can be given such a value that the pulse front (P3) appears perpendicular to the line of observation (CB), which is often advantageous for measuring purposes.

Fig. 6
Fig. 6

Light from laser L illuminates by diverging lens A the object at C and hologram plate H is illuminated by diverging lens R via mirror M. The object is observed from B which is at a distance R behind the plate. A necessary condition for holographic recording with an ultrashort pulse from A is that L1 + L2 = L3 + L4.

Fig. 7
Fig. 7

Hologram plate H reconstructs pulse front P by use of reference pulse R. The reconstructed pulse front, which moves with apparent speed υ, appears to be at P0, P1, and P2 when studied from B0, B1, and B2, respectively. When studied from B3 it appears to be at P3 and from B4 at P4. If we move B0 to an infinite distance the apparent pulse front is P. If we study the pseudoscopic image from B5 the pulse front appears to be at P5.

Fig. 8
Fig. 8

Three-dimensional shape of this propeller is measured by studying its intersection with a thin sheet of light.

Fig. 9
Fig. 9

Picosecond pulse from the laser at A is used both to illuminate the propeller (C) and to produce the reference pulse that illuminates the hologram plate (H) via mirrors M1 and M2. From B1, B2, and B3 are, during reconstruction, seen intersections S1, S2, and S3, respectively. The straightness of the intersections is an approximation which could be true only if distance HC were infinite.

Fig. 10
Fig. 10

Photo exposed during reconstruction with the camera positioned at B1 corresponding to cross section S1 (Fig. 9). The sheet of light has just reached the hub of the propeller and two of its blades.

Fig. 11
Fig. 11

Camera at B2 produced cross section S2. The hub has just passed out of the light into darkness while the four blades and their central joint are intersected.

Fig. 12
Fig. 12

Light sheet has passed the central joint and the cross sections of the blades reveal their 3-D shape.

Fig. 13
Fig. 13

Same setup as in Fig. 9 but the point of observation (camera) is not only moved along the hologram plate but also backward away from the plate as indicated by squares Bik.

Fig. 14
Fig. 14

Same hologram plate as in Figs. 1012 but studied from a point behind the plate (B21) at about half of the distance the propeller was in front of the plate during the recording. In this case intersecting surface S21 is tilted ~20°.

Fig. 15
Fig. 15

Same hologram as in Figs. 1012 but the camera was moved still further away from the plate. The intersecting plate is rotated so that it becomes parallel to a large position of one of the curved blades of the propeller.

Fig. 16
Fig. 16

While the holograms in Figs. 1015 are all made in reflection, similar methods can be used in transmission. The setup is designed to reveal an object (O) hidden between two scatterplates (B) and (F). The ultrashort laser pulse from L is reflected by mirrors M1 and M4, illuminates scatterplate B, and passes through the object (O) resulting in the broken pulse front (W) which reaches the hologram plate (H). The reference pulse is reflected by M2 and M3; N1 and N2 are two diverging lenses.

Fig. 17
Fig. 17

Light from laser L is divided into object and reference beams by the beam splitter (BS). The object beam is reflected by mirror M1 and illuminates ground glass screen S1, passes through the transparent object (C), and reaches the hologram plate (H) after passing through the second ground glass screen S2. The reference beam is reflected by mirror m2 toward the hologram plate. A necessary condition for holographic recording with an ultrashort pulse is that L1 + L2 = L3 + L4.

Fig. 18
Fig. 18

Transparent object consisting of two pieces of Plexiglas held together so that light at the top had to pass one layer, while light further down had to pass two layers of Plexiglas.

Fig. 19
Fig. 19

Setup is similar to that in Fig. 17, but the transparent object (C) is observed directly as it is illuminated by the laser pulse that has passed through ground glass S1. The angle (ϕ) of the apparent pulse front (P) is a function of the angle of light illuminating S1, the angle of the reference beam (β), and the relation of R to L4.

Fig. 20
Fig. 20

One single 8-ps pulse is delivered by the laser and the reconstruction is photographed through the left part of the hologram plate with the camera lens at a distance from the plate of ~3 cm. What we see is the first light which arrives all around the Plexiglas.

Fig. 21
Fig. 21

Photo made through the middle of the plate showing that, after the surrounding light has passed by, the light delayed by one layer of Plexiglas arrives.

Fig. 22
Fig. 22

Photo made through the right part of the plate showing how the light delayed by two layers of Plexiglas arrives.

Fig. 23
Fig. 23

Photo corresponding to Fig. 21, but the point of observation (the camera lens) is moved further away (0.3 m) from the plate. The result is that the intersecting light sheet appears to be tilted.

Fig. 24
Fig. 24

When looking at the conjugate image of the plate the tilt appears so large that we see the pulse front almost from the side in spite of the fact that it moved straight toward us during recording. The pulse front which is split into three moves from left to right and on the top we see light passing over the Plexiglas. Further down light has passed through one layer and furthest down through two layers of Plexiglas.

Fig. 25
Fig. 25

Looking through one point of the real image toward the hologram plate we see a bright line across the plate. This bright line represents the position of the reference pulse (the light shutter) at the moment when that object point was recorded. Thus the horizontal position of this line is a measure of the distance to the studied object point.

Equations (27)

Equations on this page are rendered with MathJax. Learn more.

x 2 a 2 + y 2 b 2 = 1 ,
L = a ,
L 2 = c 2 + b 2 ,
x 2 L 2 + y 2 L 2 C 2 = 1 ,
2 L = A D + D E + E B .
2 L = A D + ( y D y H ) 2 + ( x D x H ) 2 + x H 2 + y H 2 .
( x c ) 2 L 2 + y 2 L 2 C 2 = 1 ,
x H = x y H y .
( x c ) 2 { 0 , 5 [ A D + ( y D y H ) 2 + ( x y H y x D ) 2 ] + y H x 2 y 2 + 1 } 2 + y 2 { 0 , 5 [ A D + ( y D y H ) 2 + ( x y H y x D ) 2 ] + y H x 2 y 2 + 1 } 2 C 2 = 1 .
( x c ) 2 [ 0 , 5 ( A D + y D 2 + x D 2 ) ] 2 + y 2 [ 0 , 5 ( A D + y D 2 + x D 2 ) ] 2 C 2 = 1 .
( x c ) 2 [ 0 , 5 ( A D + x y H y x D ) + y H x 2 y 2 + 1 ] 2 + y 2 [ 0 , 5 ( A D + y H y x D ) + y H x 2 y 2 + 1 ] 2 C 2 = 1 .
L 1 + L 2 = L 3 + L 4 .
L 1 + L 2 = L 3 + L 4 ,
L 1 = L 1 because L 1 is independent of α ,
( L 2 ) 2 = ( R tan α ) 2 + L 2 2 2 L 2 R tan α cos ( β + 90 ) ,
( L 3 ) 2 = L 3 2 + S 2 2 L 3 S cos ( γ + 90 + ϕ ) ,
S = ( L 4 + R ) sin α cos ( α + ϕ ) ,
L 4 = ( L 4 + R ) sin ( 90 + ϕ ) sin ( α + 90 + ϕ ) R cos α .
L 2 = R tan α sin β + L 2 ,
L 3 = ( L 4 + R ) sin α cos ϕ sin ( γ + ϕ ) + L 3 ,
L 4 = ( L 4 + R ) tan α tan ϕ + L 4 .
tan ϕ = 1 1 + cos γ ( R sin β L 4 + R sin γ ) .
tan γ = R sin β 2 ( L 4 + R ) .
sin γ = R L 4 + R sin β .
sin γ = R L 4 + R sin β .
d = K + L sin ( ϕ + β ) cos β ,
d = K + L sin ϕ .

Metrics