One-step rainbow holography using a spherical mirror

Roberto Torroba; Hector J. Rabal; Mario J. Garavaglia

doi:10.1364/AO.25.003288

Applied Optics
Vol. 25,
Issue 18,
pp. 3288-3290
(1986)
•https://doi.org/10.1364/AO.25.003288

One-step rainbow holography using a spherical mirror

Roberto Torroba, Hector J. Rabal, and Mario J. Garavaglia

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Roberto Torroba, Hector J. Rabal, and Mario J. Garavaglia, "One-step rainbow holography using a spherical mirror," Appl. Opt. 25, 3288-3290 (1986)

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Abstract

A simple one-step rainbow holographic method is proposed. The optical setup requires only a slit and a spherical mirror, without a separate reference beam. Also, due to the experimental arrangement, the resulting image can be viewed by reflection. The primary aberrations of this hologram are calculated, and its advantages are discussed.

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Aberration	Formula
Spherical	$S = \frac{γ}{Z_{S}^{3}} - \frac{γ}{d^{3}} + \frac{1}{Z_{i}^{3}} - \frac{1}{Z_{R}^{3}}$
Coma	${\begin{array}{l} C_{x} = \frac{γ}{Z_{S}^{3}} X_{S} - \frac{γ}{d^{3}} X_{0} + \frac{X_{i}}{Z_{i}^{3}} - \frac{X_{R}}{Z_{R}} \\ C_{y} = \frac{γ}{Z_{S}^{3}} γ_{S} - \frac{γ Y_{0}}{d^{3}} + \frac{Y_{i}}{Z_{i}^{3}} - \frac{Y_{R}}{Z_{R}^{3}} \end{array}$
Astigmatism	${\begin{array}{l} A_{x} = γ \frac{X_{S}^{2}}{Z_{S}^{3}} - γ \frac{X_{0}^{2}}{d^{3}} + \frac{X_{i}^{2}}{Z_{i}^{3}} - \frac{X_{R}^{2}}{Z_{R}^{3}} \\ Axy = γ \frac{X_{S} Y_{S}}{Z_{S}^{3}} - γ \frac{X_{0} Y_{0}}{d^{3}} + \frac{X_{i} Y_{i}}{Z_{i}^{3}} - \frac{X_{R} Y_{R}}{Z_{R}^{3}} \\ A_{y} = γ \frac{Y_{S}^{2}}{Z_{S}^{3}} - γ \frac{Y_{0}^{2}}{d^{3}} + \frac{Y_{i}^{2}}{Z_{i}^{3}} - \frac{Y_{R}^{2}}{Z_{R}^{3}} \end{array}$
Field Curvature	$F = \frac{γ}{Z_{S}^{3}} (X_{S}^{2} + Y_{S}^{2}) - \frac{γ}{d^{3}} (X_{0}^{2} + Y_{0}^{2}) + \frac{1}{Z_{i}^{3}} (X_{i}^{2} + Y_{i}^{2}) - \frac{1}{Z_{R}^{3}} (X_{R}^{2} + Y_{R}^{2})$
Distortion	${\begin{array}{l} D_{x} = \frac{γ}{Z_{S}^{3}} X_{S}^{3} - γ \frac{X_{0}^{3}}{d^{3}} + \frac{X_{i}^{3}}{Z_{i}^{3}} - \frac{X_{R}^{3}}{Z_{R}^{3}} \\ D_{y} = \frac{γ}{Z_{S}^{3}} Y_{S}^{3} - γ \frac{Y_{0}^{3}}{d^{3}} + \frac{Y_{i}^{3}}{Z_{i}^{3}} - \frac{Y_{R}^{3}}{Z_{R}^{3}} \end{array}$

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Applied Optics