Colorimetric method for phase evaluation

Antonin Miks; Jiri Novak; Pavel Novak

doi:10.1364/JOSAA.23.000894

Journal of the Optical Society of America A
Vol. 23,
Issue 4,
pp. 894-901
(2006)
•https://doi.org/10.1364/JOSAA.23.000894

Colorimetric method for phase evaluation

Antonin Miks, Jiri Novak, and Pavel Novak

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Antonin Miks, Jiri Novak, and Pavel Novak, "Colorimetric method for phase evaluation," J. Opt. Soc. Am. A 23, 894-901 (2006)

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Abstract

Measurements of very small phase changes in optical measurement techniques are usually performed with interferometric methods that are based on evaluation of interference patterns, which correspond to a phase change of the investigated wave field. If values of the phase change are small, it is difficult to determine accurately the phase values, and one needs very expensive measurement systems. We present a simple method for evaluation of small phase variations that uses the interference of polychromatic light. The phase change affects the color of the interference pattern, and the color of the interference pattern corresponds to a specific phase change that can be evaluated using colorimetric analysis. We describe and analyze our colorimetric phase evaluation method. The proposed method offers accurate results, and it may be suitable for practical utilization in the optical industry.

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λ	$\bar{x}$	$\bar{y}$	$\bar{z}$	x	y
380	0.001	0.000	0.007	0.174	0.005
400	0.014	0.000	0.068	0.173	0.005
420	0.134	0.004	0.646	0.171	0.005
440	0.348	0.023	1.747	0.164	0.011
460	0.291	0.060	1.669	0.144	0.030
480	0.096	0.139	0.813	0.091	0.133
500	0.005	0.323	0.272	0.008	0.538
520	0.063	0.710	0.078	0.074	0.834
540	0.290	0.954	0.020	0.230	0.754
560	0.595	0.995	0.004	0.373	0.624
580	0.916	0.870	0.002	0.512	0.487
600	1.062	0.631	0.001	0.627	0.372
620	0.854	0.381	0.000	0.691	0.308
640	0.448	0.175	0.000	0.719	0.281
660	0.165	0.061	0.000	0.730	0.270
680	0.047	0.017	0.000	0.733	0.267
700	0.011	0.004	0.000	0.735	0.265
720	0.003	0.001	0.000	0.735	0.265
740	0.001	0.000	0.000	0.735	0.265
760	0.000	0.000	0.000	0.735	0.265

λ	$W (λ)$
λ	A	B	C	$D_{65}$
380	9.79	22.40	33.00	49.96
400	14.71	41.30	63.30	82.75
420	21.00	63.20	98.10	93.43
440	28.70	80.80	121.50	104.86
460	37.82	88.30	123.10	117.81
480	48.25	95.20	123.90	115.92
500	59.86	94.20	112.10	109.35
520	72.50	89.50	96.90	104.79
540	85.95	96.90	102.10	104.41
560	100.00	102.80	105.30	100.00
580	114.44	101.00	97.80	95.79
600	129.04	98.00	89.70	90.01
620	143.62	99.70	88.10	87.70
640	157.98	102.20	87.80	83.70
660	171.96	105.00	87.90	80.21
680	184.43	103.90	84.00	78.28
700	198.26	99.10	76.30	71.61
720	210.36	92.90	68.30	61.60
740	221.66	86.90	61.50	75.09
760	232.11	84.70	58.10	46.42

A (nm)	x	y	$x_{approx}$	$y_{approx}$	$δ x$ (%)	$δ y$ (%)
10	0.3640	0.1794	0.3639	0.1794	0.04	0.04
30	0.2519	0.1651	0.2485	0.1690	1.32	0.77
50	0.1889	0.1949	0.1774	0.1909	6.06	2.04
100	0.2077	0.3155	0.1690	0.3012	18.6	4.52

A (nm)	$A_{x}$ (nm)	$A_{y}$ (nm)	$A_{z}$ (nm)	$δ A_{x}$ (%)	$δ A_{y}$ (%)	$δ A_{z}$ (%)
10	9.982	9.977	9.969	0.17	0.23	0.31
30	29.22	30.60	29.24	2.60	1.99	2.54
50	40.01	50.33	46.72	20.0	0.66	6.54

λ	$\bar{x}$	$\bar{y}$	$\bar{z}$	x	y
380	0.001	0.000	0.007	0.174	0.005
400	0.014	0.000	0.068	0.173	0.005
420	0.134	0.004	0.646	0.171	0.005
440	0.348	0.023	1.747	0.164	0.011
460	0.291	0.060	1.669	0.144	0.030
480	0.096	0.139	0.813	0.091	0.133
500	0.005	0.323	0.272	0.008	0.538
520	0.063	0.710	0.078	0.074	0.834
540	0.290	0.954	0.020	0.230	0.754
560	0.595	0.995	0.004	0.373	0.624
580	0.916	0.870	0.002	0.512	0.487
600	1.062	0.631	0.001	0.627	0.372
620	0.854	0.381	0.000	0.691	0.308
640	0.448	0.175	0.000	0.719	0.281
660	0.165	0.061	0.000	0.730	0.270
680	0.047	0.017	0.000	0.733	0.267
700	0.011	0.004	0.000	0.735	0.265
720	0.003	0.001	0.000	0.735	0.265
740	0.001	0.000	0.000	0.735	0.265
760	0.000	0.000	0.000	0.735	0.265

Abstract

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Journal of the Optical Society of America A