In this paper, a new calibration method for accurate long focal-length
measurements, based on Talbot
interferometry, is presented. Error analysis is derived in detail by the
numerical method, and an effective way to improve the accuracy is proposed. By
this method, the systematic errors that are the main factors effecting accuracy
are calibrated and reduced. Both simulation and experiments have been carried
out to prove the effectiveness and advantages of the proposed method as compared
to conventional approaches. The experimental results reveal that the relative
error is lower than 0.02%, and the repeatability is better than 0.05%. This
method is especially useful for measuring long focal-length lenses.
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
Calibrated data computed are close to the assumed ones.
calibrated from Eq. (11) is also constant. The
calibration method is reasonable and effective to reduce
disturbances.
Table 2.
Experimental Data for Calibration of Measuring the Focal Lengtha
Serial Number
Angle of Moiré Fringes
Inclined Angle between Two Gratings
Serial Number
Angle of Moiré Fringes
Inclined Angle between Two Gratings
1
16.2975
0.4050
14
24.2451
0.2775
2
16.7421
0.3950
15
24.2508
0.2775
3
17.1214
0.3855
16
25.3391
0.2655
4
17.6679
0.3750
17
26.2597
0.2565
5
18.2286
0.3655
18
27.0789
0.2485
6
18.6087
0.3565
19
28.0469
0.2390
7
19.3627
0.3435
20
29.1989
0.2305
8
20.1763
0.3340
21
30.5557
0.2190
9
20.5302
0.3250
22
31.7963
0.2100
10
21.2665
0.3150
23
32.9906
0.2000
11
22.1504
0.3045
24
34.8245
0.1900
12
22.7473
0.2950
25
36.3641
0.1805
13
23.7040
0.2860
26
38.6562
0.1690
Systematic error
Systematic error
2.119
Twenty-six sets of data were caught in about 15 min. Systematic
errors and were calculated by the calibration
method discussed in the text.
The systematic errors had been calibrated. Substituting these data
into Eq. (4), the
focal length was calculated, where , . Relative accuracy is about 0.017%,
better than 0.02%. Therefore, the calibration method is effective,
and the measurement of the long focal length has high precision.
Table 4.
Experimental Results for the Repeatability of the Concave Mirror
()a
Test Times
Radius Mean
Standard Radius
Relative Error
6.25 hours
6573.8921 mm
6574 mm
0.049%
Seventy-five sets of data were fetched in about 6.25 h. The
mirror radius was calculated by Eq. (4). Relative error is
about 0.049%, lower than 0.05%. This method is insensitive to the
testing environment.
Calibrated data computed are close to the assumed ones.
calibrated from Eq. (11) is also constant. The
calibration method is reasonable and effective to reduce
disturbances.
Table 2.
Experimental Data for Calibration of Measuring the Focal Lengtha
Serial Number
Angle of Moiré Fringes
Inclined Angle between Two Gratings
Serial Number
Angle of Moiré Fringes
Inclined Angle between Two Gratings
1
16.2975
0.4050
14
24.2451
0.2775
2
16.7421
0.3950
15
24.2508
0.2775
3
17.1214
0.3855
16
25.3391
0.2655
4
17.6679
0.3750
17
26.2597
0.2565
5
18.2286
0.3655
18
27.0789
0.2485
6
18.6087
0.3565
19
28.0469
0.2390
7
19.3627
0.3435
20
29.1989
0.2305
8
20.1763
0.3340
21
30.5557
0.2190
9
20.5302
0.3250
22
31.7963
0.2100
10
21.2665
0.3150
23
32.9906
0.2000
11
22.1504
0.3045
24
34.8245
0.1900
12
22.7473
0.2950
25
36.3641
0.1805
13
23.7040
0.2860
26
38.6562
0.1690
Systematic error
Systematic error
2.119
Twenty-six sets of data were caught in about 15 min. Systematic
errors and were calculated by the calibration
method discussed in the text.
The systematic errors had been calibrated. Substituting these data
into Eq. (4), the
focal length was calculated, where , . Relative accuracy is about 0.017%,
better than 0.02%. Therefore, the calibration method is effective,
and the measurement of the long focal length has high precision.
Table 4.
Experimental Results for the Repeatability of the Concave Mirror
()a
Test Times
Radius Mean
Standard Radius
Relative Error
6.25 hours
6573.8921 mm
6574 mm
0.049%
Seventy-five sets of data were fetched in about 6.25 h. The
mirror radius was calculated by Eq. (4). Relative error is
about 0.049%, lower than 0.05%. This method is insensitive to the
testing environment.