High-resolution phase-shifting Ronchi test

Esteban Luna; Luis Salas; Erika Sohn; Elfego Ruiz; Joel Herrera; Jorge Valdez; Eduardo López; Fernando Quirós

doi:10.1364/AO.468068

Applied Optics
Vol. 61,
Issue 27,
pp. 7875-7882
(2022)
•https://doi.org/10.1364/AO.468068

High-resolution phase-shifting Ronchi test

Esteban Luna, Luis Salas, Erika Sohn, Elfego Ruiz, Joel Herrera, Jorge Valdez, Eduardo López, and Fernando Quirós

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Esteban Luna, Luis Salas, Erika Sohn, Elfego Ruiz, Joel Herrera, Jorge Valdez, Eduardo López, and Fernando Quirós, "High-resolution phase-shifting Ronchi test," Appl. Opt. 61, 7875-7882 (2022)

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Abstract

A method adding phase-shifting capacity in two mutually perpendicular axes to the Ronchi test is presented in this work. The phase of the object with the position of the reflected ray on the grating was identified and used to solve the equation of reflection in two orthogonal directions. In this manner, the test-surface figure was obtained. The procedure was demonstrated with an inverse qualitative test and a direct, quantitative test. Both tests give results comparable to Fizeau interferometry, with the precision of the order of 25 nm peak to valley. This technique is a good alternative to interferometry because, in addition to its inherent high-resolution, it is possible to obtain the radius of curvature and conic constant, which interferometers, requiring auxiliary optics, cannot provide. This method also has a high dynamic range and is not as susceptible to vibrations or turbulence. The setup can be built with low-cost, readily available components, is easily aligned, uses a white light source, and can be made very lightweight and compact, which makes it ideal for mounting onto existing polishing machines in any optical fabrication workshop, to perform in situ surface metrology.

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Supplementary Material (1)

Name	Description
Visualization 1	Simulation of a phase-shifted Ronchi test. This simulation corresponds to Fig. 3 in the manuscript.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Equations (19)

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Case	$T_{x}$ (µm)	$T_{y}$ (µm)	$A_{x}$ (µm)	$A_{y}$ (µm)	$C_{x}$ (µm)	$C_{y}$ (µm)	$K_{x}$ (µm)	$K_{y}$ (µm)	$D$ (µm)	$S$ (µm)	RMS
Ronchi	23.975	−23.711	0.070	0.079	0.053	0.044	0.009	0.000	1913	0.088	0.027
Fizeau	−0.969	−0.716	0.037	0.005	0.075	0.025	0.001	−0.001	0.859	−0.962	0.039

Parameter	Changes	$Δ T_{x}$ (µm)	$Δ T_{y}$ (µm)	$Δ A_{x}$ (µm)	$Δ A_{y}$ (µm)	$Δ C_{x}$ (µm)	$Δ C_{y}$ (µm)	$Δ K_{x}$ (mm)	$Δ K_{y}$ (µm)	$Δ D$ (mm)	$Δ S$ (µm)
$Δ x_{s 0}$	1 mm	−22.633	−0.000	−0.001	0.000	−0.022	0.000	0.000	0.000	0.007	0.000
$Δ y_{s 0}$	1 mm	−0.000	22.633	0.001	0.000	0.000	0.022	−0.000	0.000	−0.000	0.000
$Δ z_{s 0}$	1 mm	0.007	−0.007	0.000	0.000	0.000	0.000	0.000	0.000	0.593	0.001
$Δ x_{r 0}$	1 mm	−22.636	−0.000	−0.001	0.000	−0.022	−0.000	0.000	0.000	0.007	0.000
$Δ y_{r 0}$	1 mm	0.000	22.632	0.001	0.000	0.000	0.022	0.000	−0.000	−0.000	0.000
$Δ z_{r 0}$	1 mm	0.008	−0.007	0.000	−0.000	0.000	0.000	0.000	0.000	0.601	0.000
$Δ x_{m 0}$	1 mm	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
$Δ y_{m 0}$	1 mm	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
$Δ z_{m 0}$	1 mm	−0.015	0.015	−0.000	0.000	−0.000	−0.000	0.000	0.000	−1.194	−0.001
$β$	0.1 deg	−0.000	0.010	−0.000	−0.035	0.000	−0.001	0.000	−0.000	0.000	0.000

Case	$T_{x}$ (µm)	$T_{y}$ (µm)	$A_{x}$ (µm)	$A_{y}$ (µm)	$C_{x}$ (µm)	$C_{y}$ (µm)	$K_{x}$ (µm)	$K_{y}$ (µm)	$D$ (µm)	$S$ (µm)	RMS
Ronchi	23.975	−23.711	0.070	0.079	0.053	0.044	0.009	0.000	1913	0.088	0.027
Fizeau	−0.969	−0.716	0.037	0.005	0.075	0.025	0.001	−0.001	0.859	−0.962	0.039

Parameter	Changes	$Δ T_{x}$ (µm)	$Δ T_{y}$ (µm)	$Δ A_{x}$ (µm)	$Δ A_{y}$ (µm)	$Δ C_{x}$ (µm)	$Δ C_{y}$ (µm)	$Δ K_{x}$ (mm)	$Δ K_{y}$ (µm)	$Δ D$ (mm)	$Δ S$ (µm)
$Δ x_{s 0}$	1 mm	−22.633	−0.000	−0.001	0.000	−0.022	0.000	0.000	0.000	0.007	0.000
$Δ y_{s 0}$	1 mm	−0.000	22.633	0.001	0.000	0.000	0.022	−0.000	0.000	−0.000	0.000
$Δ z_{s 0}$	1 mm	0.007	−0.007	0.000	0.000	0.000	0.000	0.000	0.000	0.593	0.001
$Δ x_{r 0}$	1 mm	−22.636	−0.000	−0.001	0.000	−0.022	−0.000	0.000	0.000	0.007	0.000
$Δ y_{r 0}$	1 mm	0.000	22.632	0.001	0.000	0.000	0.022	0.000	−0.000	−0.000	0.000
$Δ z_{r 0}$	1 mm	0.008	−0.007	0.000	−0.000	0.000	0.000	0.000	0.000	0.601	0.000
$Δ x_{m 0}$	1 mm	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
$Δ y_{m 0}$	1 mm	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
$Δ z_{m 0}$	1 mm	−0.015	0.015	−0.000	0.000	−0.000	−0.000	0.000	0.000	−1.194	−0.001
$β$	0.1 deg	−0.000	0.010	−0.000	−0.035	0.000	−0.001	0.000	−0.000	0.000	0.000

Abstract

Supplementary Material (1)

Data availability

Cited By

Figures (7)

Tables (2)

Equations (19)

Applied Optics