Light-in-flight recording. 2: Compensation for the limited speed of the light used for observation

Nils Abramson

doi:10.1364/AO.23.001481

Applied Optics
Vol. 23,
Issue 10,
pp. 1481-1492
(1984)
•https://doi.org/10.1364/AO.23.001481

Light-in-flight recording. 2: Compensation for the limited speed of the light used for observation

Nils Abramson

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Nils Abramson, "Light-in-flight recording. 2: Compensation for the limited speed of the light used for observation," Appl. Opt. 23, 1481-1492 (1984)

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Abstract

Equations are given for the apparent rotation and distortion of wave fronts caused by the limited speed of the light used for the observation (here referred to as a relativistic effect). Methods are discussed and mathematically derived for the compensation and the elimination of these unwanted effects. Equations are given for how these effects can be used to advantage for the manipulation of the tilt angle of the intersecting plane used in contouring. Optimization of the time resolution and the time capacity for a certain length of hologram plate is given in tabular form. A new formula is enunciated for the curvature of the relativistically distorted wave front. Finally, it is demonstrated that the ellipsoids of the holodiagram are the spherical wave fronts from a point of illumination as they are seen in a scattering medium from another point of observation.

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t (sec)	t · c (m)	D (m)	sineγ	T	n
2 × 10⁻¹⁵	6 × 10⁻⁷	1.2 ×	57 × 10⁻⁸	19 × 10⁻¹⁶	0.81
10⁻¹⁴	3 × 10⁻⁶	2.1 × 10⁻¹	14 × 10⁻⁶	48 × 10⁻¹⁵	4.8
10⁻¹³	3 × 10⁻⁵	2.1 × 10⁻²	14 × 10⁻⁴	48 × 10⁻¹³	48
10⁻¹²	3 × 10⁻⁴	2.1 × 10⁻³	14 × 10⁻²	48 × 10⁻¹¹	480
2.7 × 10⁻¹²	8.1 × 10⁻⁴	8.1 × 10⁻⁴	1	33 × 10⁻¹⁰	1250
10⁻¹¹	3 × 10⁻³	2.1 × 10⁻⁴	1	33 × 10⁻¹⁰	333
10⁻¹⁰	3 × 10⁻²	2.1 × 10⁻⁵	1	33 × 10⁻¹⁰	33
10⁻⁹	3 × 10⁻¹	2.1 × 10⁻⁶	1	33 × 10⁻¹⁰	3.3

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Equations (35)

Applied Optics