Real-time depth measurement and display using Fresnel diffraction and white-light processing

James R. Leger; Michael A. Snyder

doi:10.1364/AO.23.001655

Applied Optics
Vol. 23,
Issue 10,
pp. 1655-1670
(1984)
•https://doi.org/10.1364/AO.23.001655

Real-time depth measurement and display using Fresnel diffraction and white-light processing

James R. Leger and Michael A. Snyder

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James R. Leger and Michael A. Snyder, "Real-time depth measurement and display using Fresnel diffraction and white-light processing," Appl. Opt. 23, 1655-1670 (1984)

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Abstract

An optical method of measuring and displaying depth information has been developed which is based on the Fresnel diffraction properties of coherently illuminated gratings. Cosine modulated gratings are found to be more flexible than simple gratings for depth measurement. A pair of gratings crossed at right angles is used to provide two independent depth measurement channels. A real-time white-light processor has been developed to convert the depth information into pseudocolor. The depth signal is input to a white-light processor by a liquid crystal light valve. The two depth channels are filtered to produce different color images such that the hue of the combined image is a function of depth.

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L (Object field width)	$Z_{U} (Range) \frac{9 L^{2}}{8 λ S^{2}}$	$A (Aspect ratio) \frac{9 L}{8 λ S^{2}}$
1 mm	0.028 mm	0.028
5 mm	0.71 mm	0.14
10 mm	2.8 mm	0.28
50 mm	71.0 mm	1.4
100 mm	280.0 mm	2.8
500 mm	7.1 m	14.
1m	28.m	28.
5m	710. m	140.

L (Object field width)	$d_{1} (Modulation period) (mm) \frac{3 L}{S}$	f₁ (Modulation frequency) (lines/mm)
1 mm	0.012	83.
5 mm	0.060	17.
10 mm	0.12	8.3
50 mm	0.60	1.7
100 mm	1.2	0.83
500 mm	6.0	0.17
1 m	12.	0.083
5 m	60.	0.017

A (Aspect ratio)	$d_{0} (Carrier period) (\frac{8 λ S}{3}) A$	f₀ (Carrier frequency) (lines/mm)
0.005	2.1 μm	470.
0.01	4.2 μm	240.
0.05	21. μm	47.
0.1	42. μm	24.
0.5	0.21 mm	4.7
1.0	0.42 mm	2.4
5.0	2.1 mm	0.47

Wavelength	λ = 0.6328 × 10⁻³ mm
Grating period	d₀ = 0.254 mm
Grating frequency	f₀ = 3.937 lines/mm
Talbot period (measured)	Z_T_(meas) = 203 mm ± 1 mm
Talbot period (calculated)	Z_T = 204 mm
Repetition distance (calculated)	Z_R = 102 mm
Unambiguous range (calculated)	Z_U = 51 mm
Focal length of camera lens	f_l = 50 mm
Numerical aperture (object side)	N.A.= 0.035
Depth of field (calculated)	l = 7.3 mm
Depth of field (measured)	l_(meas) = 6.2 mm ± 1 mm
Object field width	L = 21 mm
Aspect ratio	A = 2.43
Space–bandwidth product of illumination	S_i = 83
Space–bandwidth product of camera	S = 124
Magnification (from object to light valve)	M = 1.5

Wavelength	λ = 0.6328 × 10⁻³ mm
Ronchi period	d = 0.254 mm
Equivalent grating carrier frequency	f₀ = 21.65 lines/mm
Equivalent grating modulation frequency	f₁ = 1.97 lines/mm
Pseudo-Talbot period (measured)	Z_T_(meas) = 18.56 mm ± 0.1 mm
Pseudo-Talbot period (calculated)	Z_T = 18.54 mm
Repetition period (calculated)	Z_R = 9.27 mm
Unambiguous Talbot range (calculated)	Z_U = 4.63 mm
Focal length of camera lens	f_l = 50 mm
Diffraction-limited lens aperture	a_y = 0.26 mm
Diffraction-limited numerical aperture	N.A. = 0.00124
Diffraction-limited depth of field	l = 204 mm
Diffraction-limited number of repetition ranges	N = 22
Actual lens aperture	a_x = 28 mm
Width of horizontal slit over lens	a_y = 1.3 mm
x Numerical aperture (object side)	N.A._x = 0.11
y Numerical aperture (object side)	N.A._y = 0.0061
Depth of field-y direction (calculated)	l = 41.4 mm
Calculated number of repetition distances	N = 4.5
Observed number of repetition distances	N_(meas) = 5
Object field width	L = 21 mm
Aspect ratio	A = 0.22
Space–bandwidth product of illumination	S_i = 82
Space–bandwidth product of camera	S = 124
Magnification (from object to light valve)	M = 1.5

Abstract

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Figures (13)

Tables (5)

Equations (52)

Applied Optics