Abstract

A novel coherent imaging method analogous to electronic differential amplification is described and analyzed. The method is well suited to highlighting local changes in the optical properties of a dynamic object whose more prominent details are largely static. The object may be examined either in transmitted light or in reflected light. The method discriminates between changes that result from substructural reorganization of object details too fine to be imaged as resolved structures and changes that result from the microdisplacement of optically resolved structures. Substructural reorganization is signaled by changes in the amplitude of the transmitted or reflected light, whereas ordinary displacement is displayed in the usual way through a change in phase. The method is capable of detecting displacements as small as several milliwavelengths. Images of contractile activity in muscle are presented that illustrate the method’s sensitivity and analytic power.

© 1985 Optical Society of America

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References

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  1. R. L. Powell, K. A. Stetson, “Interferometric vibration analysis by wavefront reconstruction,” J. Opt. Soc. Am. 55, 1593–1598 (1965).
    [CrossRef]
  2. L. O. Heflinger, R. F. Wuerker, R. E. Brooks, “Holographic interferometry,” J. Appl. Phys. 37, 642–649 (1966).
    [CrossRef]
  3. K. A. Haines, B. P. Hildebrand, “Surface deformation measurement using the wavefront reconstruction technique,” Appl. Opt. 5, 595–602 (1966).
    [CrossRef] [PubMed]
  4. C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).
  5. W. Schumann, M. Dubas, Holographic Interferometry (Springer-Verlag, Berlin, 1979).
    [CrossRef]
  6. R. Jones, C. Wykes, Holographic Speckle Interferometry (Cambridge U. Press, Cambridge, 1983), particularly Chaps. 3–5.
  7. K. Høgmoen, O. J. Løkberg, “Detection and measurement of small vibrations using electronic speckle pattern interferometry,” Appl. Opt. 16, 1869–1875 (1977).
    [CrossRef] [PubMed]
  8. D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, “Optical image synthesis (complex amplitude addition and subtraction) by holographic Fourier transformation,” Phys. Lett. 18, 116–118 (1965).
    [CrossRef]
  9. M. Sharnoff, R. W. Henry, D. M. J. Bellezza, “Holographic visualization of the nerve impulse,” Biophys. J. 21, 109(A) (1978).
  10. M. Sharnoff, T. H. Karcher, L. P. Brehm, “Microdifferential holography and the polysarcomeric unit of activation of skeletal muscle,” Science 223, 822–825 (1984).
    [CrossRef] [PubMed]
  11. R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), especially Chap. 10.
  12. J. F. Hamilton, “Reciprocity law failure” in The Theory of the Photographic Process, 3rd. ed., T. H. James, ed. (Macmillan, New York, 1966).
  13. The author has found that some holographic emulsions may fail this test in exposures of submillisecond duration, where, when the overall exposure does not exceed that which produces the brightest additive image, the positively unbalanced differential images appear to be systematically stronger than the negatively unbalanced ones. It would seem from the direction of this effect that hypersensitization and latensification12 lie at its origin. It is plausible that, when practical necessity requires exposure flashes so short as to cause reciprocity failure, well-planned departure from the equal-∊ rule may still secure the result that (I+ − I−) is independent of phase shifts in the subject wave.
  14. N. Bloembergen, E. M. Purcell, R. V. Pound, “Relaxation effects in nuclear magnetic resonance absorption,” Phys. Rev. 73, 679–712 (1948) (especially pp. 684–685).
    [CrossRef]
  15. Jenkins and White, Fundamentals of Optics, 2nd. ed. (McGraw-Hill, New York, 1950).
  16. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  17. M. Born, E. Wolf, Principles of Optics, 3rd. ed. (Pergamon, Oxford, 1965), especially pp. 128–132.
  18. M. Born, E. Wolf, Principles of Optics, 3rd. ed. (Pergamon, Oxford, 1965), pp. 651–652.
  19. Because every nonvanishing even order is missing from the Fraunhofer diffraction pattern of a Ronchi grating, this value of |Φ/q| is smaller than it would be in many other cases. Grating examples exist for which |Φ/q| is larger than the value given by Eq. (22).
  20. In the spirit of the Rayleigh criterion,15 the sensitivity of the human eye has been arbitrarily taken to permit discrimination of temporally steady spatial variations of about 20%. The factor of ½ used here is appropriate because visual comparison of Iδ against I−δ is twice as sensitive as comparison of Iδ against the mean, ½(Iδ+ I−). The estimate made here is actually quite conservative, for the eye is really much more sensitive to sharp intensity gradients than Rayleigh assumed (see Ref. 19). The comparison of images or illumination intensities by means of the split-field comparator exploits this high sensitivity in a striking way.
  21. M. Alpern, “The eyes and vision,” in Handbook of Optics, W. G. Driscoll, ed. (McGraw-Hill, New York, 1978), especially Secs. 17 and 18.
  22. D. S. Smith, Muscle (Academic, New York, 1972).
  23. M. Sharnoff, L. P. Brehm, R. W. Henry, “Dynamic structures through microdifferential holography,” Biophys. J. (to be published).

1984 (1)

M. Sharnoff, T. H. Karcher, L. P. Brehm, “Microdifferential holography and the polysarcomeric unit of activation of skeletal muscle,” Science 223, 822–825 (1984).
[CrossRef] [PubMed]

1978 (1)

M. Sharnoff, R. W. Henry, D. M. J. Bellezza, “Holographic visualization of the nerve impulse,” Biophys. J. 21, 109(A) (1978).

1977 (1)

1966 (2)

L. O. Heflinger, R. F. Wuerker, R. E. Brooks, “Holographic interferometry,” J. Appl. Phys. 37, 642–649 (1966).
[CrossRef]

K. A. Haines, B. P. Hildebrand, “Surface deformation measurement using the wavefront reconstruction technique,” Appl. Opt. 5, 595–602 (1966).
[CrossRef] [PubMed]

1965 (2)

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, “Optical image synthesis (complex amplitude addition and subtraction) by holographic Fourier transformation,” Phys. Lett. 18, 116–118 (1965).
[CrossRef]

R. L. Powell, K. A. Stetson, “Interferometric vibration analysis by wavefront reconstruction,” J. Opt. Soc. Am. 55, 1593–1598 (1965).
[CrossRef]

1948 (1)

N. Bloembergen, E. M. Purcell, R. V. Pound, “Relaxation effects in nuclear magnetic resonance absorption,” Phys. Rev. 73, 679–712 (1948) (especially pp. 684–685).
[CrossRef]

Alpern, M.

M. Alpern, “The eyes and vision,” in Handbook of Optics, W. G. Driscoll, ed. (McGraw-Hill, New York, 1978), especially Secs. 17 and 18.

Bellezza, D. M. J.

M. Sharnoff, R. W. Henry, D. M. J. Bellezza, “Holographic visualization of the nerve impulse,” Biophys. J. 21, 109(A) (1978).

Bloembergen, N.

N. Bloembergen, E. M. Purcell, R. V. Pound, “Relaxation effects in nuclear magnetic resonance absorption,” Phys. Rev. 73, 679–712 (1948) (especially pp. 684–685).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 3rd. ed. (Pergamon, Oxford, 1965), especially pp. 128–132.

M. Born, E. Wolf, Principles of Optics, 3rd. ed. (Pergamon, Oxford, 1965), pp. 651–652.

Brehm, L. P.

M. Sharnoff, T. H. Karcher, L. P. Brehm, “Microdifferential holography and the polysarcomeric unit of activation of skeletal muscle,” Science 223, 822–825 (1984).
[CrossRef] [PubMed]

M. Sharnoff, L. P. Brehm, R. W. Henry, “Dynamic structures through microdifferential holography,” Biophys. J. (to be published).

Brooks, R. E.

L. O. Heflinger, R. F. Wuerker, R. E. Brooks, “Holographic interferometry,” J. Appl. Phys. 37, 642–649 (1966).
[CrossRef]

Brumm, D.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, “Optical image synthesis (complex amplitude addition and subtraction) by holographic Fourier transformation,” Phys. Lett. 18, 116–118 (1965).
[CrossRef]

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), especially Chap. 10.

Collier, R. J.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), especially Chap. 10.

Dubas, M.

W. Schumann, M. Dubas, Holographic Interferometry (Springer-Verlag, Berlin, 1979).
[CrossRef]

Funkhouser, A.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, “Optical image synthesis (complex amplitude addition and subtraction) by holographic Fourier transformation,” Phys. Lett. 18, 116–118 (1965).
[CrossRef]

Gabor, D.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, “Optical image synthesis (complex amplitude addition and subtraction) by holographic Fourier transformation,” Phys. Lett. 18, 116–118 (1965).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Haines, K. A.

Hamilton, J. F.

J. F. Hamilton, “Reciprocity law failure” in The Theory of the Photographic Process, 3rd. ed., T. H. James, ed. (Macmillan, New York, 1966).

Heflinger, L. O.

L. O. Heflinger, R. F. Wuerker, R. E. Brooks, “Holographic interferometry,” J. Appl. Phys. 37, 642–649 (1966).
[CrossRef]

Henry, R. W.

M. Sharnoff, R. W. Henry, D. M. J. Bellezza, “Holographic visualization of the nerve impulse,” Biophys. J. 21, 109(A) (1978).

M. Sharnoff, L. P. Brehm, R. W. Henry, “Dynamic structures through microdifferential holography,” Biophys. J. (to be published).

Hildebrand, B. P.

Høgmoen, K.

Jones, R.

R. Jones, C. Wykes, Holographic Speckle Interferometry (Cambridge U. Press, Cambridge, 1983), particularly Chaps. 3–5.

Karcher, T. H.

M. Sharnoff, T. H. Karcher, L. P. Brehm, “Microdifferential holography and the polysarcomeric unit of activation of skeletal muscle,” Science 223, 822–825 (1984).
[CrossRef] [PubMed]

Lin, L. H.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), especially Chap. 10.

Løkberg, O. J.

Pound, R. V.

N. Bloembergen, E. M. Purcell, R. V. Pound, “Relaxation effects in nuclear magnetic resonance absorption,” Phys. Rev. 73, 679–712 (1948) (especially pp. 684–685).
[CrossRef]

Powell, R. L.

Purcell, E. M.

N. Bloembergen, E. M. Purcell, R. V. Pound, “Relaxation effects in nuclear magnetic resonance absorption,” Phys. Rev. 73, 679–712 (1948) (especially pp. 684–685).
[CrossRef]

Restrick, R.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, “Optical image synthesis (complex amplitude addition and subtraction) by holographic Fourier transformation,” Phys. Lett. 18, 116–118 (1965).
[CrossRef]

Schumann, W.

W. Schumann, M. Dubas, Holographic Interferometry (Springer-Verlag, Berlin, 1979).
[CrossRef]

Sharnoff, M.

M. Sharnoff, T. H. Karcher, L. P. Brehm, “Microdifferential holography and the polysarcomeric unit of activation of skeletal muscle,” Science 223, 822–825 (1984).
[CrossRef] [PubMed]

M. Sharnoff, R. W. Henry, D. M. J. Bellezza, “Holographic visualization of the nerve impulse,” Biophys. J. 21, 109(A) (1978).

M. Sharnoff, L. P. Brehm, R. W. Henry, “Dynamic structures through microdifferential holography,” Biophys. J. (to be published).

Smith, D. S.

D. S. Smith, Muscle (Academic, New York, 1972).

Stetson, K. A.

Stroke, G. W.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, “Optical image synthesis (complex amplitude addition and subtraction) by holographic Fourier transformation,” Phys. Lett. 18, 116–118 (1965).
[CrossRef]

Vest, C. M.

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 3rd. ed. (Pergamon, Oxford, 1965), pp. 651–652.

M. Born, E. Wolf, Principles of Optics, 3rd. ed. (Pergamon, Oxford, 1965), especially pp. 128–132.

Wuerker, R. F.

L. O. Heflinger, R. F. Wuerker, R. E. Brooks, “Holographic interferometry,” J. Appl. Phys. 37, 642–649 (1966).
[CrossRef]

Wykes, C.

R. Jones, C. Wykes, Holographic Speckle Interferometry (Cambridge U. Press, Cambridge, 1983), particularly Chaps. 3–5.

Appl. Opt. (2)

Biophys. J. (1)

M. Sharnoff, R. W. Henry, D. M. J. Bellezza, “Holographic visualization of the nerve impulse,” Biophys. J. 21, 109(A) (1978).

J. Appl. Phys. (1)

L. O. Heflinger, R. F. Wuerker, R. E. Brooks, “Holographic interferometry,” J. Appl. Phys. 37, 642–649 (1966).
[CrossRef]

J. Opt. Soc. Am. (1)

Phys. Lett. (1)

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, “Optical image synthesis (complex amplitude addition and subtraction) by holographic Fourier transformation,” Phys. Lett. 18, 116–118 (1965).
[CrossRef]

Phys. Rev. (1)

N. Bloembergen, E. M. Purcell, R. V. Pound, “Relaxation effects in nuclear magnetic resonance absorption,” Phys. Rev. 73, 679–712 (1948) (especially pp. 684–685).
[CrossRef]

Science (1)

M. Sharnoff, T. H. Karcher, L. P. Brehm, “Microdifferential holography and the polysarcomeric unit of activation of skeletal muscle,” Science 223, 822–825 (1984).
[CrossRef] [PubMed]

Other (15)

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), especially Chap. 10.

J. F. Hamilton, “Reciprocity law failure” in The Theory of the Photographic Process, 3rd. ed., T. H. James, ed. (Macmillan, New York, 1966).

The author has found that some holographic emulsions may fail this test in exposures of submillisecond duration, where, when the overall exposure does not exceed that which produces the brightest additive image, the positively unbalanced differential images appear to be systematically stronger than the negatively unbalanced ones. It would seem from the direction of this effect that hypersensitization and latensification12 lie at its origin. It is plausible that, when practical necessity requires exposure flashes so short as to cause reciprocity failure, well-planned departure from the equal-∊ rule may still secure the result that (I+ − I−) is independent of phase shifts in the subject wave.

Jenkins and White, Fundamentals of Optics, 2nd. ed. (McGraw-Hill, New York, 1950).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

M. Born, E. Wolf, Principles of Optics, 3rd. ed. (Pergamon, Oxford, 1965), especially pp. 128–132.

M. Born, E. Wolf, Principles of Optics, 3rd. ed. (Pergamon, Oxford, 1965), pp. 651–652.

Because every nonvanishing even order is missing from the Fraunhofer diffraction pattern of a Ronchi grating, this value of |Φ/q| is smaller than it would be in many other cases. Grating examples exist for which |Φ/q| is larger than the value given by Eq. (22).

In the spirit of the Rayleigh criterion,15 the sensitivity of the human eye has been arbitrarily taken to permit discrimination of temporally steady spatial variations of about 20%. The factor of ½ used here is appropriate because visual comparison of Iδ against I−δ is twice as sensitive as comparison of Iδ against the mean, ½(Iδ+ I−). The estimate made here is actually quite conservative, for the eye is really much more sensitive to sharp intensity gradients than Rayleigh assumed (see Ref. 19). The comparison of images or illumination intensities by means of the split-field comparator exploits this high sensitivity in a striking way.

M. Alpern, “The eyes and vision,” in Handbook of Optics, W. G. Driscoll, ed. (McGraw-Hill, New York, 1978), especially Secs. 17 and 18.

D. S. Smith, Muscle (Academic, New York, 1972).

M. Sharnoff, L. P. Brehm, R. W. Henry, “Dynamic structures through microdifferential holography,” Biophys. J. (to be published).

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

W. Schumann, M. Dubas, Holographic Interferometry (Springer-Verlag, Berlin, 1979).
[CrossRef]

R. Jones, C. Wykes, Holographic Speckle Interferometry (Cambridge U. Press, Cambridge, 1983), particularly Chaps. 3–5.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of instrumentation for microdifferential holography. Single lines represent electrical pathways.

Fig. 2
Fig. 2

Geometry of incident beam, scattered wavelet, and small object that lies near the focal point of the objective lens.

Fig. 3
Fig. 3

Lateral displacement of object from position O to position O′ causes a change in the length of the optical path followed by the scattered wavelet. The displacement has been greatly exaggerated with respect to the scale of Fig. 2.

Fig. 4
Fig. 4

Interferometric sensitivity to displacement of a Rayleigh scatterer versus numerical aperture of objective lens. Scatterer displaced along y axis (Figs. 2 and 3). Dotted lines, incident light π polarized; solid curves, incident light σ polarized. Upper pair of curves, θi = Θ; lower pair of curves, sin θi = ½ sin Θ.

Fig. 5
Fig. 5

Interferometric sensitivity to displacement of a Rayleigh scatterer displaced along the z axis (Fig. 3). Dotted curves, incident light π polarized; solid curves, incident light σ polarized. Upper curves, θi = Θ; lower curves, sin θi = ½ sin Θ. Curves for θi = 0 lie close to the upper curves but correspond to opposite sign, and |Φ/q| nearly vanishes when sinθi ≈ (1/3)sin Θ.

Fig. 6
Fig. 6

Scene printed under normal (left-hand panel) and high (right-hand panel) contrast from a single negative of a nondifferential holographic image of a portion of a resting fiber dissected from frog semitendinosus muscle. The microscope objective had a numerical aperture of 0.75, and it was focused upon the lower edge of the fiber. The value of sin θi was 0.16, with the incident beam lying in the plane formed by the optical axis and the fiber axis. The white bar in the right-hand panel represents a distance of 50 μm. The spacing of the cross striations was 2.05 μm. The dark curved lines at the upper-right-hand corner of each panel are the diffraction pattern of a scratch on the bottom of the specimen chamber.

Fig. 7
Fig. 7

Holographically reconstituted images of the fiber portion shown in Fig. 6, as viewed under the same illumination, objective, plane of focus, magnification, and integrated exposure. D is a positively unbalanced control image of the resting fiber. A, B, and C are, respectively, a difference image, a negatively unbalanced differential image, and a positively unbalanced differential image of the activated fiber. The value || chosen during exposure of the unbalanced holograms was 0.15. The four reconstituted images were photographed and printed under identical conditions. The holograms for A, B, and C were not made simultaneously but during a sequence of contractions elicited by individual current pulses each applied at the same point during the holographic exposure cycle that, itself, was common to all the holograms. Experience has shown10 that the contractions and holograms are highly repeatable. Fiber reference, 508.

Equations (26)

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g ( x , y ) = Γ ( x , y ) f ( x , y ) .
Γ ( x , y ) = [ 1 + μ ( x , y ) ] exp [ i Φ ( x , y ) ] ,
A ( x , y ) = { 1 [ 1 + μ ( x , y ) ] exp [ i Φ ( x , y ) ] } f ( x , y )
I ( x , y ) = | A ( x , y ) | 2 ,
I 0 ( x , y ) = | f ( x , y ) + f ( x , y ) | 2 ,
I ( x , y ) / I 0 ( x , y ) = ½ { [ 1 + μ ( x , y ) ] [ 1 cos Φ ( x , y ) + ½ μ 2 } .
A + ( x , y ) = ( 1 + ) f ( x , y ) ( 1 ) g ( x , y ) = { ( 1 + ) ( 1 ) [ 1 + μ ( x , y ) ] × exp [ i Φ ( x , y ) ] } f ( x , y )
I + ( x , y ) = { 2 ( 1 + 2 ) [ 1 + μ ( x , y ) ] [ 1 cos Φ ( x , y ) ] + [ 2 ( 1 ) μ ( x , y ) ] 2 } | f ( x , y ) | 2 ,
A ( x , y ) = ( 1 ) f ( x , y ) ( 1 + ) g ( x , y )
I ( x , y ) = { 2 ( 1 + 2 ) [ 1 + μ ( x , y ) ] [ 1 cos Φ ( x , y ) ] + [ 2 + ( 1 + ) μ ( x , y ) ] 2 } | f ( x , y ) | 2 .
I ± δ ( x , y ) = 4 ( [ 1 + μ ( x , y ) ] sin 2 { ½ [ Φ ( x , y ) ± 2 π δ ] } + ¼ μ 2 ( x , y ) ) | f ( x , y ) | 2 .
s λ / 2 n sin Θ = λ / 2 N.A. ,
Φ = 2 π Δ / λ = ( 4 n π q sin Θ ) / λ .
| q min | λ Φ min / 4 π N.A. = s Φ min / 2 π ,
S = α F ( θ , ϕ ; θ i ) ,
f = α 0 Θ 0 2 π F ( θ , ϕ , θ i ) sin θ d ϕ d θ .
Δ ( q , θ , ϕ ; θ i ) = n [ q x sin θ cos ϕ + q y ( sin θ sin ϕ sin θ i ) + q z ( cos θ cos θ i ) ] .
g = α 0 Θ 0 2 π F ( θ , ϕ ; θ i ) { exp [ ( 2 π i / λ ) × Δ ( q , θ , ϕ ; θ i ) ] } sin θ d ϕ d θ .
g = f [ 1 + ( 2 π i / λ f ) 0 Θ 0 2 π F ( θ , ϕ ; θ i ) × Δ ( q , θ , ϕ , θ i ) sin θ d ϕ d θ ] .
F π = { 1 [ sin θ i cos θ + cos θ i sin θ sin ϕ ] 2 } 1 / 2 ,
F σ = { 1 [ sin θ cos ϕ ] 2 } 1 / 2 ,
Φ = ( 2 π / λ ) ( n q y sin θ i ) .
Φ = ( q / w ) [ 1 + ( 1 ) j 2 j 1 ] / [ 1 + ( 2 / π ) j ( 1 ) j / ( 2 j + 1 ) ] ,
Φ = ( 2 n q sin Θ ) / [ ( 1 + 2 / π ) λ ] .
2 / 20 000 I min ( x , y ) / I 0 ( x , y ) Φ min 2 / 4 ;
I ± δ ( x , y ) 2 π δ [ 2 π δ ± 2 Φ ( x , y ) ] | f ( x , y ) | 2 .

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