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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 1, Iss. 5 — May. 5, 2006
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Testing of steep convex aspheric surface with a Hartmann sensor by using a CGH

Ho-Soon Yang, Jae-Bong Song, In-Won Lee, and Yun-Woo Lee  »View Author Affiliations


Optics Express, Vol. 14, Issue 8, pp. 3247-3254 (2006)
http://dx.doi.org/10.1364/OE.14.003247


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Abstract

Most aspheric surfaces have been tested by interferometer with some null correctors. This approach, however, often fails when there are many aspherical terms or test surface is very steep because it is not easy to design the conventional null lens or CGH (Computer Generated Hologram). On the other hand, 3-D profilometer can measure aspheric surfaces without any null correctors; however, it takes some time to measure, which makes it unsuitable for the production line in the factory. In this paper, we apply the Hartmann test to the measurement of steep convex aspheric surfaces of which diameter is about 16 mm. In order to increase the measurement accuracy, we calibrated the test setup using a CGH that simulates the ideal test surface. We demonstrated that the significant amount of error in the test setup could be removed by this calibration process. The test results showed only 2 nm rms WFE (wave front error) difference even though the WFE of test setup was worsened by more than 0.13 μm rms. Since this method makes it possible to measure highly aspheric surface quickly and accurately, it can be used in the production line.

© 2006 Optical Society of America

1. Introduction

There are at least three typical testing methods for aspheric surfaces; 3-D profilometers, null tests[1

1. D. Malacara, “Null tests using compensators,” in Optical shop testing (Wiley, New York, 1992), Ch. 12.

], and the Hartmann test[2

2. D. Malacara, “Hartmann and other screen tests,” in Optical shop testing (Wiley, New York, 1992), Ch. 10.

]. The 3-D profilometer like the UA3P from Panasonic does not need any null correctors and can be used for the rough surface and smooth surfaces. However, it has a dimensional limitation and takes some time while tracing the surface. Therefore, it is not suitable for a fast measurement. Instead, the null test or Hartmann test is more suitable for a fast measurement as it takes a picture of whole surface in a short time. The null test, particularly using a CGH (computer generated hologram) has been successfully applied to test difficult surfaces. Burge tested 1.15 m diameter convex surfaces with a CGH [3

3. J. H. Burge, “Fizeau interferometry for large convex surfaces,” in Optical manufacturing and testing, V. J. Doherty and H. P. Stahl, eds., Proc. SPIE 2536, 127–138 (1995). [CrossRef]

]. Kim et al. used a CGH with alignment sectors to test highly curved paraboloids of which diameter is 90 mm and f-number is only 0.76 [4

4. T. H. Kim, J. Burge, Y. W. Lee, and S. S. Kim, “Null test for highly paraboloidal mirror,” Appl. Opt. 43, 3614–3618 (2004). [CrossRef] [PubMed]

]. The Hartmann test has also been used for the test of aspheric optics. Zverev et al. tested a 6-m mirror by using a Hartmannn pattern. When there was 6 μm of surface deformation, the measurement error of this method was approximately 0.02 μm, compared to the interferometric measurement [5

5. V. A. Zverev, S. A. Rodionov, M. N. Sokol′skii, and V. V. Usoskin, “Testing of the primary mirror of the LAT (large azimuthal telescope) by the Hartmann method during its manufacture,” Sov. J. Opt. Technol. 44, 127–129 (1977).

]. Yang et al. tested a 0.9-m aspheric mirror using a Hartmann sensor with a null corrector to increase the dynamic range [6

6. H.-S. Yang, Y.-W. Lee, J.-B. Song, and I.-W. Lee, “Null hartmann test for the fabrication of large aspheric surfaces,” Opt. Express 13, 1839–1847 (2005). www.opticsexpress.org/abstract.cfm?cfm?URI=OPEX-13-6-1839 [CrossRef] [PubMed]

]. This method made it possible to measure a whole surface from the early polishing stage (38.6 μm peak-to-valley (PV) error) to the near final polishing stage (1.06 μm PV) without additional instruments. On the other hand, Pfund et al. measured 6 mm aspheric surface with 63.9 λ PV error (λ=633 nm) within the accuracy of λ/500 PV error by compensating the errors in the test setup after the measurement [7

7. J. Pfund, N. Lindlein, and J. Schwider, “Misalignment effects of the Shack-Hartmann sensor,” Appl. Opt. 37, 22–27 (1998). [CrossRef]

, 8

8. J. Pfund, N. Lindlein, and J. Schwider, ℌNonnull testing of rotationally symmetric aspheres: a systematic error assessment,” Appl. Opt. 40, 439–446 (2001). [CrossRef]

]. Jeong et al. measured the lower and higher order WFE of conventional toric, multifocal, and customized soft contact lenses which are submerged in a wet cell [9

9. T. M. Jeong, M. Menon, and G. Yoon, “Measurement of wave-front aberration in soft contact lenses by use of a Shack-Hartmsnn wave-front sensor,” Appl. Opt. 44, 4523–4527 (2005). [CrossRef] [PubMed]

].

In the research described below, we developed a new method to measure a small convex aspheric surface with steep slopes. The key point is to calibrate the whole testing setup using some ideal test surface and set this data as a reference to be used in the measurement of the real target. We do not need to analyze those errors; instead, if we detect any deviations from the reference, we can construct the deformation of the test surface. The Hartmann sensor would be the best to detect deviations because its wave front sensing is based on the relative displacements of beam spots with respect to their reference. In this way, this method can provide a fast and accurate measurement for the aspheric surface and be used in the production line of the factory. However, one major problem in this concept is how to procure a highly accurate test surface. We propose that a CGH can be the best ideal test surface since we can design the CGH to reflect the light to the desired direction as an ideal test surface will do. The manufacturing accuracy is comparable to that of an e-beam machine of which line accuracy is on the order of sub micrometer.

Figure 1 shows a schematic testing setup for a small, convex aspheric surface. This setup is quite similar to that described by Yang et al [6

6. H.-S. Yang, Y.-W. Lee, J.-B. Song, and I.-W. Lee, “Null hartmann test for the fabrication of large aspheric surfaces,” Opt. Express 13, 1839–1847 (2005). www.opticsexpress.org/abstract.cfm?cfm?URI=OPEX-13-6-1839 [CrossRef] [PubMed]

]. The interferometer generates a collimated beam. This beam passes through the beam expander and condensing lenses and illuminates the whole surface of test surface. After reflection, the test surface is imaged on both the Hartmann sensor and the interferometer. Before measuring the test surface, a CGH that simulates the ideal target is measured by Hartmann sensor and the positions of each beam spot are stored in the computer as a reference. Then, the test surface is mounted instead of a CGH and measured again by the Hartmann sensor. The deformation of surface is determined by displacements of beam spots with respect to a reference. Even though the measurement is carried out on the Hartmann sensor, the interferometer is essential not only because it supplies the light source to the Hartmann sensor, but also because we need to align a CGH with respect to the optical setup accurately.

Fig. 1. Optical layout for the measurement of small aspheric surface.

2. Testing method for an uncoated steep convex asphere

Even though a CGH is not suitable for a null corrector in our case, we can use it as an ideal target in the test setup. We can design a CGH to reflect the light to the desired direction as an ideal target will do. By measuring a CGH with the Hartmann sensor, we can estimate all error sources in test setup like Fig.1, including the manufacturing and alignment errors. The positions of each beam spot on the Hartmann sensor result from all kinds of test errors and can be used as a reference. This is the calibration process for the test setup. After finishing this calibration process, we measure the test surface in the same test setup. Then, we can reconstruct the deformation of the test surface by calculating the relative displacement of the spots with respect to the reference. The interferometer cannot be used for this purpose because the non-null test setup usually generates a large WFE that is beyond the dynamic range of the interferometer.

The Hartmann sensor we used in the experiment has 35×40 small apertures. Each aperture is 142 μm in diameter and is separated from its neighbor by 350 μm. The distance between the Hartmann mask and the CCD is 10.923 mm. The sensing area of CCD is 12.57 mm × 14.34 mm and its pixel size is 14 μm × 14 μm. According to the geometry of the Hartmann sensor, the theoretical maximum measurable wave front slope has the following relation [6

6. H.-S. Yang, Y.-W. Lee, J.-B. Song, and I.-W. Lee, “Null hartmann test for the fabrication of large aspheric surfaces,” Opt. Express 13, 1839–1847 (2005). www.opticsexpress.org/abstract.cfm?cfm?URI=OPEX-13-6-1839 [CrossRef] [PubMed]

]:

f(Wx)max=S21.22λfd
(1)

wherefis the distance between the apertures and the CCD, S is the aperture spacing, d is the diameter of the aperture, and λ. is 0.6328 μm. The maximum measurable wave front slope of the sensor is approximately 10.6 mrad.

Fig. 2. The asphericity of the surface. Wave means 633 nm.

To illuminate the test surface, we need to design a proper optical system which consists of beam expander and condensing lenses, which is shown in Fig. 1. A beam from the interferometer is expanded to have a 100 mm diameter using a beam expander with magnification of 10. This beam illuminates the target through condensing lenses that consist of four single lenses. The theoretical WFE of the test setup is reduced to 16λ PV from 46λ PV of original asphericity, which is shown in Fig. 3. In this figure, the WFE slope is a maximum 45 mrad, which is beyond the dynamic range of Hartmann sensor used in our experiment. This large residual WFE is not critical for the accurate measurement in our method, which is explained in detail in section 3.

Fig. 3. (a). Wave front error of the test setup and (b) its slope in radian.

3. Preliminary characterization

Fig. 4. Measurement result of high precision doublet using a Hartmann sensor as the doublet is defocused. The reference was generated at defocus of 20 mm. (a) rms WFE measured (b) residual error after linear fitting.

4. Testing

As an ideal target, an on-axis and amplitude type CGH was prepared, which is shown in Fig. 5 (a). The CGH is a chrome-on-glass type in third-order reflection mode. According to the manufacturer, there are three kinds of error in the fabrication of a CGH; 0.01λ rms of substrate flatness error, 0.015 μm rms of origin of coordinates, and 0.04 μm rms of trajectory of rotation error. Among them, the combination of origin of coordinates and trajectory of rotation errors is about 0.043 μm rms. This error corresponds to 0.018λ rms of WFE, considering that the CGH pattern spacing is 3.03 μm rms. This means that the WFE induced by the fabrication error of a CGH is quite small compared to the measurement target accuracy (0.1λ rms) and a CGH can be used to calibrate the test setup.

It has a main CGH part to simulate the surface to be measured and an alignment CGH part for aligning itself with respect to the system. The alignment portion is essential to eliminate any alignment errors in the system. Figure 5(b) is the test surface to be measured. This was made of Zerodur for thermal stability and manufactured using diamond turning machine (DTM). Figure 6 is a profile error of the test surface, which was measured by a 3-D profiler. Some overall form error and high peak irregular shapes in the central part can be seen. These irregular shapes come from a partial polishing process after the DTM work. The spatial period of irregular shapes is minimum 0.5 mm. Considering that the image size of test surface is 8.76 mm (magnification is 0.55) and the separation of apertures on the Hartmann sensor is 0.35 mm, these irregular shapes would not be reconstructed properly.

Fig. 5 (a) CGH as an ideal surface, (b) Test surface to be measured.
Fig. 6. Surface error measured by 3-D profiler, UA3P from Panasonic Co.

Actually, in order to have enough margins for the accurate measurement, it is important to locate the spot away from the boundary of its sub-aperture so that the conventional reconstruction algorithm works properly. For this, we adjusted the positions of sub-aperture cells by changing the offset of position and number of cells in the software. Figure 7 shows the reference generated by measuring the CGH in the testing setup. In this figure, the minimum distance between the center of spot and boundary of sub-aperture is only 0.04 mm (at circle A in Fig. 7), which is too close to the boundary. This short distance may give the incorrect reconstruction if there is some further deformation at the test surface. To ensure an accurate reconstruction, we confined the aperture size to 7.7 mm (88% of the clear aperture). This region is shown in Fig. 7 as circle B. This will give the capability of measuring few μm deviation of test surface from the ideal.

Figure 8(a) shows the measured WFE of the beam expander by the interferometer. The four elements in the condensing lenses would add additional WFE to the error in the beam expander, 0.08 μm rms. Figure 8(b) is the measurement result using reference generated by measuring CGH. The coarse WFE from 35 × 40 cells was interpolated using a cubic spline fitting. This picture shows the main feature of test surface profile error. Even though the detail of the central part in Fig. 6 is not revealed, the concave shape is similar to the averaged central portion. The PV error is 1.627 μm and rms error is 0.163 μm, which is only 16 nm rms higher than that of 3-D profiler. This slight difference may come from the average of detail structure of the central part in the Hartmann sensor measurement and different measurement area.

Fig. 7. Reference generated by measuring CGH. Spot in circle A is the closest to the boundary of sub-aperture. Circle B is the measurement area of test surface.

In Fig. 8, it was not clear how much the WFE in the test setup was removed in the measurement of the test surface. To check this, the beam expander was intentionally defocused to generate 0.21 μm rms error, which is shown in Fig. 9(a). The CGH was aligned using an interferometer again and the new reference was generated on the Hartmann sensor. The test surface was measured again with respect to this new reference. Figure 9(b) shows the measurement result of the test surface. Even though beam expander showed significant defocus aberration compared to Fig. 8(a), the test surface error was quite close to Fig. 8(b) and the difference in rms WFE was only 2 nm. This means that the error in test setup can be significantly removed by the calibration with a CGH.

Fig. 8. Measurement result of test surface (a) WFE of the beam expander, and (b) surface profile of the test surface (z-unit is micrometer).
Fig. 9. Measurement result after intentional misalignment of beam expander (a) WFE of the beam expander, and (b) surface profile of the test surface (z-unit is micrometer).

5. Concluding remarks

We proposed a new method to test the steep aspheric convex surfaces, using a combination of a Hartmann test with a CGH. The CGH is served as a reference surface and the test setup is calibrated using this CGH. Then, the measurement accuracy is significantly increased as the error in the test setup is considerably removed. Experimentally, the test surface error was changed by only 2 nm rms even though the error in the beam expander in the test setup was increased 0.13 μm rms. Also, this measurement result was within 16 nm rms compared to that of 3-D profilometer. Since this method makes it possible to measure highly aspheric surfaces quickly and accurately, we expect to use it in the production line environments.

Currently, we are modifying the reconstruction software of the Hartmann sensor to make it possible to control the size and location of each sub-aperture separately. By the manual control in the software, we can make each beam spot positioned near the center of corresponding sub-aperture wherever they are located on the sensor. This can increase the dynamic range of the test setup, which makes it possible to measure steeper aspheric surface or some free form surfaces.

Acknowledgments

We thank to Dr. Gun-Hee Kim at KBSI for generating the test surface and Dr. Sang-Suk Kim at KOPTI for the surface measurement using the UA3P. The discussions with Dell Olsen at Spiricon, Inc. for the generation of reference file in the Hartmann sensor were valuable, as well.

References and links

1.

D. Malacara, “Null tests using compensators,” in Optical shop testing (Wiley, New York, 1992), Ch. 12.

2.

D. Malacara, “Hartmann and other screen tests,” in Optical shop testing (Wiley, New York, 1992), Ch. 10.

3.

J. H. Burge, “Fizeau interferometry for large convex surfaces,” in Optical manufacturing and testing, V. J. Doherty and H. P. Stahl, eds., Proc. SPIE 2536, 127–138 (1995). [CrossRef]

4.

T. H. Kim, J. Burge, Y. W. Lee, and S. S. Kim, “Null test for highly paraboloidal mirror,” Appl. Opt. 43, 3614–3618 (2004). [CrossRef] [PubMed]

5.

V. A. Zverev, S. A. Rodionov, M. N. Sokol′skii, and V. V. Usoskin, “Testing of the primary mirror of the LAT (large azimuthal telescope) by the Hartmann method during its manufacture,” Sov. J. Opt. Technol. 44, 127–129 (1977).

6.

H.-S. Yang, Y.-W. Lee, J.-B. Song, and I.-W. Lee, “Null hartmann test for the fabrication of large aspheric surfaces,” Opt. Express 13, 1839–1847 (2005). www.opticsexpress.org/abstract.cfm?cfm?URI=OPEX-13-6-1839 [CrossRef] [PubMed]

7.

J. Pfund, N. Lindlein, and J. Schwider, “Misalignment effects of the Shack-Hartmann sensor,” Appl. Opt. 37, 22–27 (1998). [CrossRef]

8.

J. Pfund, N. Lindlein, and J. Schwider, ℌNonnull testing of rotationally symmetric aspheres: a systematic error assessment,” Appl. Opt. 40, 439–446 (2001). [CrossRef]

9.

T. M. Jeong, M. Menon, and G. Yoon, “Measurement of wave-front aberration in soft contact lenses by use of a Shack-Hartmsnn wave-front sensor,” Appl. Opt. 44, 4523–4527 (2005). [CrossRef] [PubMed]

10.

R. Diaz-Uribe and M. Campos-Garcia, “Null-screen testing of fast convex aspheric surfaces,” Appl. Opt. 39, 2670–2677 (2000). [CrossRef]

11.

M. Campos-Garcia, R. Diaz-Uribe, and F. Granados-Agustin, “Testing fast aspheric convex surfaces with a linear array of sources,” Appl. Opt. 43, 6255–6264 (2004). [CrossRef] [PubMed]

12.

W. H. Southwell, “Wavefront estimation fromm wavefront slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980). [CrossRef]

OCIS Codes
(090.1760) Holography : Computer holography
(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: February 23, 2006
Revised Manuscript: March 31, 2006
Manuscript Accepted: April 11, 2006
Published: April 17, 2006

Virtual Issues
Vol. 1, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Ho-Soon Yang, Jae-Bong Song, In-Won Lee, and Yun-Woo Lee, "Testing of steep convex aspheric surface with a Hartmann sensor by using a CGH," Opt. Express 14, 3247-3254 (2006)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-14-8-3247


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References

  1. D. Malacara, "Null tests using compensators," in Optical shop testing (Wiley, New York, 1992), Ch. 12.
  2. D. Malacara, "Hartmann and other screen tests," in Optical shop testing (Wiley, New York, 1992), Ch. 10.
  3. J. H. Burge, "Fizeau interferometry for large convex surfaces," in Optical manufacturing and testing, V.J.Doherty, and H.P.Stahl, eds., Proc. SPIE 2536, 127-138 (1995). [CrossRef]
  4. T. H. Kim, J. Burge, Y. W. Lee, and S.S. Kim, "Null test for highly paraboloidal mirror," Appl. Opt. 43, 3614-3618 (2004). [CrossRef] [PubMed]
  5. V. A. Zverev, S. A. Rodionov, M. N. Sokol'skii, and V. V. Usoskin, "Testing of the primary mirror of the LAT (large azimuthal telescope) by the Hartmann method during its manufacture," Sov. J. Opt. Technol. 44, 127-129 (1977).
  6. H.-S. Yang, Y.-W. Lee, J.-B. Song, and I.-W. Lee, "Null Hartmann test for the fabrication of large aspheric surfaces," Opt. Exp., 1839-1847 (2005). [CrossRef] [PubMed]
  7. J. Pfund, N. Lindlein, and J. Schwider, "Misalignment effects of the Shack-Hartmann sensor," Appl. Opt. 37, 22-27 (1998). [CrossRef]
  8. J. Pfund, N. Lindlein, and J. Schwider, "Nonnull testing of rotationally symmetric aspheres: a systematic error assessment," Appl. Opt. 40, 439-446 (2001). [CrossRef]
  9. T. M. Jeong, M. Menon, and G. Yoon, "Measurement of wave-front aberration in soft contact lenses by use of a Shack-Hartmsnn wave-front sensor," Appl. Opt. 44, 4523-4527 (2005). [CrossRef] [PubMed]
  10. R. Diaz-Uribe, and M. Campos-Garcia, "Null-screen testing of fast convex aspheric surfaces," Appl. Opt. 39, 2670-2677 (2000). [CrossRef]
  11. M. Campos-Garcia, R. Diaz-Uribe, and F. Granados-Agustin, "Testing fast aspheric convex surfaces with a linear array of sources," Appl. Opt. 43, 6255-6264 (2004). [CrossRef] [PubMed]
  12. W. H. Southwell, "Wavefront estimation fromm wavefront slope measurements," J. Opt. Soc. Am. 70, 998-1006 (1980). [CrossRef]

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