Space-invariant multiple-grating interferometers in holography

B. J. Chang; E. N. Leith

doi:10.1364/JOSA.69.000689

Journal of the Optical Society of America
Vol. 69,
Issue 5,
pp. 689-696
(1979)
•https://doi.org/10.1364/JOSA.69.000689

Space-invariant multiple-grating interferometers in holography

B. J. Chang and E. N. Leith

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B. J. Chang and E. N. Leith, "Space-invariant multiple-grating interferometers in holography," J. Opt. Soc. Am. 69, 689-696 (1979)

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Abstract

Properties of multiple-grating interferometers in forming holograms are described. With these interferometers, the coherence requirements of off-axis holography can be reduced to a level considerably less than those of in-line holography. The effect of source coherence (or source structure) on the hologram modulation transfer function of the system is discussed. The modulation transfer function can be adjusted to produce low-pass, bandpass, or high-pass characteristics.

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Case	Object beam order	Reference beam order	Beams recombination criterion	β_xo	K_o	Broad source centering criterion	Maximum passband criterion
a	00	00		0	0	x_o = 0	x_o = 0
						y_o = 0	y_o = 0
b	0+	0+		−f₂	$(d_{4} - d_{2}) f_{2}^{2} + d_{s} f_{2}^{2}$	x_o = (d₂ − d₄)λ_o	x_o = (d₂ − d₄ − d_s)f₂λ_o
						y_o = 0	y_o = 0
c	+−	+−		−f₁ + f₂	$2 (d_{2} - d_{4}) f_{1} f_{2} + (d_{4} - d_{2} f_{2}^{2} + d_{s} {(f_{1} - f_{2})}^{2}$	x_o = (d₄ − d₂)λ_o	x_o = −d_sf₁λ_o + (d₄ − d₂ + d_s)f₂λ_o
						y_o = 0	y_o = 0
d	00	+−	f₂ > f₁	0	$d_{1} f_{1}^{2} - 2 d_{4} f_{1} f_{2} + d_{4} f_{2}^{2}$	x_o = (d₄f₂ − d₁f₁)λ_o	x_o = (d_rf₂ − d₁f₁)λ_o
						y_o = 0	y_o = 0
e	0+	+−	2f₂ > f₁	−f₂	$d_{1} f_{1}^{2} - 2 d_{4} f_{1} f_{2} + (d_{4} - d_{2}) f_{2}^{2} + d_{s} f_{2}^{2}$	x_o = [(d₄ + d₂)f₂ − d₁f₁]λ_o	x_o = −d₁f₁λ_o + (d₂ + d₄ − d_s)f₂λ_o
						y_o = 0	y_o = 0
f	+−	00	f₂ > f₁	−f₁ + f₂	$- d_{1} f_{1}^{2} + 2 d_{2} f_{1} f_{2} - d_{2} f_{2}^{2} + d_{s} {(f_{1} - f_{2})}^{2}$	x_o = (d₁f₁ − d₂f₂)λ_o	x_o = (d₁ − d_s)f₁λ_o + (d_s − d₂)f₂λ_o
						y_o = 0	y_o = 0
g	+−	0+	2f₂ > f₁	−f₁ + f₂	$- d_{1} f_{1}^{2} + 2 d_{2} f_{1} f_{2} + (d_{4} - d_{2}) f_{2}^{2} + d_{s} {(f_{1} - f_{2})}^{2}$	x_o = [d₁f₁ − (d₄ + d₂)f₂]λ_o	x_o = (d₁ − d_s)f₁λ_o + (d₂ + d_s − d₄)f₂λ_o
						y_o = 0	y_o = 0
h	+−	−+	f₂ > f₁	−f₁ + f₂	$2 (d_{2} - d_{4}) f_{1} f_{2} + (d_{4} - d_{2}) f_{2}^{2} + d_{s} {(f_{1} - f_{2})}^{2}$	x_o = [2d₁f₁ − (d₄ + d₂)f₂]λ_o	x_o = (2d₁ − d_s)f₁λ_o + (d₂ − d₂ − d₄)f₂λ_o
						y_o = 0	y_o = 0

Abstract

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Equations (51)

Journal of the Optical Society of America