Analysis and Verification of Ellipticalization Phenomenon in Transmission Tolansky Interference Rings

Zijie Xu; Baowu Zhang; Ling Zhu; Zhenyuan Fang; Xianhuan Luo; Yi Sun; Bin Zhang

doi:10.3788/AOS241242

Acta Optica Sinica, Volume. 45, Issue 1, 0126001(2025)

Analysis and Verification of Ellipticalization Phenomenon in Transmission Tolansky Interference Rings

Zijie Xu, Baowu Zhang^*, Ling Zhu, Zhenyuan Fang, Xianhuan Luo, Yi Sun, and Bin Zhang

Author Affiliations

College of Metrology Measurement and Instrument, China Jiliang University, Hangzhou 310018, Zhejiang , China

show less

Abstract Get PDF(in Chinese)

Figures & Tables(22)

Fig. 1. Tolansky interference. (a) Schematic diagram; (b) interference ring

Download full size

Fig. 2. Transmission Tolansky interferometric system. (a) Meridian structure; (b) simulated interference concentric ring

Download full size

Fig. 3. System sagittal surface structure

Download full size

Fig. 4. Simulation diagrams of parallel flat circular rings with different thicknesses. (a) 5 mm; (b) 40 mm; (c) 80 mm; (d) 120 mm

Download full size

Fig. 5. Zemax horizontal correlation illuminance curve along center of circle

Download full size

Fig. 6. Curve of eccentricity varying with parallel plate thickness

Download full size

Fig. 7. Curve of eccentricity varying with incident angle of light

Download full size

Fig. 8. Curve of eccentricity varying with distance between detector and point light source

Download full size

Fig. 9. Comprehensive influence of detector position and parallel plate thickness on eccentricity

Download full size

Fig. 10. Solidworks modeling of transmissive Tolansky interferometric system

Download full size

Fig. 11. Experimental images at different incident angles. (a) 0°; (b) 45°

Download full size

Table 1. Matlab and Zemax simulation parameters 1
View table
Table 1. Matlab and Zemax simulation parameters 1
Parameter Value
I /（°） 45
θ /（°） 1
f /mm 600
d₂ /mm 20
n₁ 1.500
n₂ 1.500
CCD size /（mm×mm） 12.8×12.8
CCD resolution /（pixel×pixel） 5120×5120

Table 2. Calculation results of circular eccentricity for different parallel plate thicknesses

View table

Table 2. Calculation results of circular eccentricity for different parallel plate thicknesses

d /mm	$e_{1}^{'}$	$e_{2}^{'}$	$e_{3}^{'}$	$\bar{e^{'}}$	$e^{'}$	Relative error /%
5	0.0648	0.0672	0.0662	0.0661	0.0667	0.900
10	0.0958	0.0926	0.0942	0.0942	0.0949	0.738
15	0.1162	0.1171	0.1160	0.1164	0.1166	0.172
20	0.1332	0.1338	0.1401	0.1357	0.1350	0.518
40	0.1922	0.1917	0.1902	0.1914	0.1918	0.208
60	0.2341	0.2345	0.2338	0.2341	0.2358	0.707
80	0.2730	0.2722	0.2716	0.2723	0.2732	0.329
100	0.3036	0.3060	0.3019	0.3038	0.3059	0.686
120	0.3366	0.3340	0.3346	0.3351	0.3369	0.534
140	0.3644	0.3647	0.3621	0.3637	0.3651	0.383
160	0.3857	0.3886	0.3892	0.3878	0.3916	0.970
180	0.4128	0.4128	0.4134	0.4130	0.4168	0.912
200	0.4361	0.4364	0.4398	0.4374	0.4406	0.726

Table 3. Matlab and Zemax simulation parameters 2
View table
Table 3. Matlab and Zemax simulation parameters 2
Parameter Value
d₁ /mm 100
θ /（°） 1
f /mm 600
d₂ /mm 20
n₁ 1.500
n₂ 1.500
CCD size /（mm×mm） 12.8×12.8
CCD resolution /（pixel×pixel） 5120×5120

Table 4. Calculation results of circular eccentricity at different incidence angles

View table

Table 4. Calculation results of circular eccentricity at different incidence angles

I /（°）	$e_{1}^{'}$	$e_{2}^{'}$	$e_{3}^{'}$	$\bar{e^{'}}$	$e^{'}$	Relative error /%
15	0.0982	0.0960	0.0909	0.0950	0.0955	0.523
30	0.1977	0.1970	0.1976	0.1974	0.1978	0.202
45	0.3036	0.3060	0.3019	0.3038	0.3059	0.686
60	0.4128	0.4152	0.4131	0.4137	0.4151	0.337
75	0.4990	0.4976	0.4989	0.4985	0.5006	0.419

Table 5. Matlab and Zemax simulation parameters 3
View table
Table 5. Matlab and Zemax simulation parameters 3
Parameter Value
d₁ /mm 100
θ /（°） 1
I /（°） 45
d₂ /mm 20
n₁ 1.500
n₂ 1.500

Table 6. Calculation results of circular eccentricity at different detector positions

View table

Table 6. Calculation results of circular eccentricity at different detector positions

f /mm	$e_{1}^{'}$	$e_{2}^{'}$	$e_{3}^{'}$	$\bar{e^{'}}$	$e^{'}$	Relative error /%
300	0.4418	0.4421	0.4423	0.4421	0.4435	0.316
400	0.3845	0.3761	0.3785	0.3797	0.3798	0.026
500	0.3318	0.3438	0.3348	0.3368	0.3374	0.178
600	0.3056	0.3041	0.3036	0.3044	0.3067	0.750
700	0.2797	0.2808	0.2834	0.2813	0.2830	0.601
800	0.2747	0.2534	0.2602	0.2628	0.2641	0.492

Table 7. Partial parameters of experiment
View table
Table 7. Partial parameters of experiment
Parameter Value
Temperature /℃ 20
Atmos /Pa 1×10⁵
Refractive index of air 1.0003
CCD size /（mm×mm） 12.8×12.8
CCD resolution /（pixel×pixel） 5120×5120
Material refractive index 1.5163

Table 8. Experimental results of eccentricity varying with plate thickness
View table
Table 8. Experimental results of eccentricity varying with plate thickness
Thickness /mm $e_{1}^{'}$ $e_{2}^{'}$ $e_{3}^{'}$ $\bar{e^{'}}$ $e^{'}$ Relative error /%
50 0.2142 0.2133 0.2138 0.2138 0.2146 0.3728
100 0.3028 0.3066 0.3152 0.3082 0.3062 0.6532
150 0.3711 0.3689 0.3792 0.3731 0.3783 1.3746
200 0.4288 0.4486 0.4352 0.4375 0.4405 0.6810

Table 9. Experimental results of eccentricity varying with incident angle
View table
Table 9. Experimental results of eccentricity varying with incident angle
Incidence angle /（°） $e_{1}^{'}$ $e_{2}^{'}$ $e_{3}^{'}$ $\bar{e^{'}}$ $e^{'}$ Relative error /%
15 0.0922 0.1022 0.0916 0.0953 0.0959 0.6256
30 0.2022 0.1944 0.1913 0.1960 0.1974 0.7092
45 0.3054 0.3046 0.3026 0.3042 0.3056 0.4581

Table 10. Experimental results of eccentricity varying with distance between detector and point light source

View table

Table 10. Experimental results of eccentricity varying with distance between detector and point light source

Distance f /mm	$e_{1}^{'}$	$e_{2}^{'}$	$e_{3}^{'}$	$\bar{e^{'}}$	$e^{'}$	Relative error /%
300	0.4468	0.4496	0.4382	0.4449	0.4433	0.3609
400	0.3708	0.3886	0.3732	0.3775	0.3796	0.5532
500	0.3396	0.3326	0.3349	0.3357	0.3372	0.4448
600	0.3022	0.3016	0.3066	0.3035	0.3064	0.9465

Table 11. Error analysis of experimental data with d₁=50 mm
View table
Table 11. Error analysis of experimental data with d₁=50 mm
Serial number $e_{i}^{'}$ $v_{i}$ $v_{i}^{2}$
1 0.2142 +0.0004 0.00000016
2 0.2133 -0.0005 0.00000025
3 0.2138 0 0
Handle
$\sum_{i = 1}^{3} e^{'} = 0.6413$
$\bar{e^{'}} = 0.2138$
$\sum_{i = 1}^{3} v_{i} = - 0.0001$ $\sum_{i = 1}^{3} v_{i}^{2} = 0.00000041$

Tools

Get Citation

Copy Citation Text

Zijie Xu, Baowu Zhang, Ling Zhu, Zhenyuan Fang, Xianhuan Luo, Yi Sun, Bin Zhang. Analysis and Verification of Ellipticalization Phenomenon in Transmission Tolansky Interference Rings[J]. Acta Optica Sinica, 2025, 45(1): 0126001

Download Citation

EndNote(RIS)BibTex Plain Text

Set citation alerts for article

Save article for my favorites

Paper Information

Category: Physical Optics

Received: Jul. 3, 2024

Accepted: Sep. 18, 2024

Published Online: Jan. 16, 2025

The Author Email: Baowu Zhang (zhangbaowu@126.com)

DOI:10.3788/AOS241242

CSTR:32393.14.AOS241242

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Matlab and Zemax simulation parameters 1

Table 1. Matlab and Zemax simulation parameters 1

Table 2. Calculation results of circular eccentricity for different parallel plate thicknesses

Table 2. Calculation results of circular eccentricity for different parallel plate thicknesses

Table 3. Matlab and Zemax simulation parameters 2

Table 3. Matlab and Zemax simulation parameters 2

Table 4. Calculation results of circular eccentricity at different incidence angles

Table 4. Calculation results of circular eccentricity at different incidence angles

Table 5. Matlab and Zemax simulation parameters 3

Table 5. Matlab and Zemax simulation parameters 3

Table 6. Calculation results of circular eccentricity at different detector positions

Table 6. Calculation results of circular eccentricity at different detector positions

Table 7. Partial parameters of experiment

Table 7. Partial parameters of experiment

Table 8. Experimental results of eccentricity varying with plate thickness

Table 8. Experimental results of eccentricity varying with plate thickness

Table 9. Experimental results of eccentricity varying with incident angle

Table 9. Experimental results of eccentricity varying with incident angle

Table 10. Experimental results of eccentricity varying with distance between detector and point light source

Table 10. Experimental results of eccentricity varying with distance between detector and point light source

Table 11. Error analysis of experimental data with d1=50 mm

Table 11. Error analysis of experimental data with d1=50 mm

Table 11. Error analysis of experimental data with d₁=50 mm

Table 11. Error analysis of experimental data with d₁=50 mm