## Inhomogeneity measurement at oblique incidence by phase measuring interferometers |

Optics Express, Vol. 21, Issue 18, pp. 20730-20737 (2013)

http://dx.doi.org/10.1364/OE.21.020730

Acrobat PDF (1613 KB)

### Abstract

The huge power solid-state lasers require large optical materials with high quality. The inhomogeneity must be required to be measured. Inhomogeneity measurement is often done at normal incidence by interferometer, while the size of large blanks is limited to the interferometer aperture. A five-step method to measure refractive index inhomogeneity over the interferometer aperture is proposed in this paper. The variation of the refractive index inhomogeneity of the glass blank is directly calculated using five interferograms measured at oblique incidence. The high repeatability of the results is given. The reliability of the method is further verified by comparing the same part measured at normal incidence.

© 2013 OSA

## 1. Introduction

1. J. H. Campbell, R. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. Whitman, J. Yu, M. Runkel, M. Riley, M. Feit, and R. Hackel, “NIF Optical materials and fabrication technologies: an overview,” Proc. SPIE **5341**, 84–101 (2004). [CrossRef]

3. F. Twyman and J. W. Perry, “The determination of Poisson’s ratio and of the absolute stress-variation of refractive index,” Proc. Phys. Soc. Lond. **34**(1), 151–154 (1921). [CrossRef]

4. F. E. Roberts and P. Langenbeck, “Homogeneity evaluation of very large disks,” Appl. Opt. **8**(11), 2311–2314 (1969). [CrossRef] [PubMed]

5. J. Schwider, R. Burow, K.-E. Elssner, R. Spolaczyk, and J. Grzanna, “Homogeneity testing by phase sampling interferometry,” Appl. Opt. **24**(18), 3059–3061 (1985). [CrossRef] [PubMed]

6. L. L. Deck, “Multiple surface phase shifting interferometry,” Proc. SPIE **4451**, 424–431 (2001). [CrossRef]

5. J. Schwider, R. Burow, K.-E. Elssner, R. Spolaczyk, and J. Grzanna, “Homogeneity testing by phase sampling interferometry,” Appl. Opt. **24**(18), 3059–3061 (1985). [CrossRef] [PubMed]

7. J. Park, L. Chen, Q. Wang, and U. Griesmann, “Modified Roberts-Langenbeck test for measuring thickness and refractive index variation of silicon wafers,” Opt. Express **20**(18), 20078–20089 (2012). [CrossRef] [PubMed]

8. D. Schönfeld, T. Reuter, R. Takke, and S. Thomas, “Stitching oil-on interferometry of large fused silica blanks,” Proc. SPIE **5965**, 59650V, 59650V-8 (2005). [CrossRef]

9. R. Jedamzik, J. Hengst, F. Elsmann, C. Lemke, T. Döhring, and P. Hartmann, “Optical materials for astronomy from SCHOTT: the quality of large components,” Proc. SPIE **7018**, 70180O, 70180O-10 (2008). [CrossRef]

## 2. Description of the method

^{−3}rad so that the reflections from the different surfaces of sample can be separated on the detector plane.

_{1}, T

_{2}, A and B, respectively. The Interferogram Scale Factor of 0.5 is used during five-step measurement. Their relationships are deduced as following: where Z

_{1}and Z

_{2}are the surface deviations of the auxiliary mirror TF and RF, Z

_{2f}is the horizontally flipped data set of Z

_{2}, Z

_{a}and Z

_{b}are the front and the back surface deviations of test part, respectively. The direction is defined in Fig. 1. Δn

_{1}and Δn

_{2}are the variations of the refractive index corresponded to the different transmissions of the second and the third measurement; d is the mean depth of the test part; θ is incident angle and θ′ is refractive angle in glass; Z

_{a}′ is the data set of Z

_{a}with a horizontal shift of x

_{0}, and x

_{0}is the displacement on X direction between the light input and output of the front surface of the test part in the fifth measurement. x

_{0}is expressed as Eq. (7).

_{a}, Z

_{a}′ and Z

_{b}respectively. T

_{1}, T

_{2}and B relate to same Z

_{b}. So there is only one variable Z

_{b}shown as Eqs. (3), (4) and (6). Then inhomogeneity at direction OQ can be solved by eliminating influence of direction PQ.

_{2}can be solved by eliminating the variables Z

_{1}, Z

_{2}, Z

*, Z*

_{2f}_{a}, Z

_{a}′, Z

_{b}and Δn

_{1}. It is written as following:

_{2}is the deviation from mean refractive index n

_{0}when the light passes through the path of the third step. If the incident angle θ is the working angle the result is expressed as the condition in situ.

## 3. Experiments and discussion

_{1}and Z

_{2}) are all better than 53nm (PV). The test sample is a fused silica glass with the dimensions of 428mm × 428mm × 54.7 mm. The mean refractive index n

_{0}is 1.5.

_{1}, T

_{2}, A and B is recorded by the interferometer, respectively. It is easy to determine whether the surface under test corresponds to the front surface or the back one. When one touch the back surface with a finger, the back surface fringes will change slightly. The incident angle θ is chosen to be 28 degree. The value is guaranteed by a mask edited on the MASK interface of the application. The horizontal length of the mask

*lm*is calculated as Eq. (9).where

*l*is the horizontal length of the test part,

*d*is the depth of the test part, θ is the incident angle. In the second and the third measurement, the test part is so placed that the horizontal shadow of the test part in the light is equal to

*lm*. Then the incident angle equals to θ. The accuracy of θ can be evaluated by length measurements of the empty cavity.

_{2}is calculated from Eq. (8) by the commercial software of Zygo corp. It is also conveniently obtained using other technical computing software.

_{1}, T

_{2}, A and B in five-step procedure are shown in Fig. 3, respectively. Inhomogeneity map Δn

_{2}calculated from Eq. (8) is shown in Fig. 4, and the horizontal size of 34.7 cm is decided by the size X in Fig. 3 (e). Therefore, the final Horizontal dimension of 39.3 cm is retrieved by the size divided by cos28°.

^{−5}, and the repeatability (1σ) of the PV is 1.4 × 10

^{−7}. Inhomogeneity RMS is 1.43 × 10

^{−6}, and the repeatability of RMS is 1 × 10

^{−8}. The measured length of the test part is the size X divided by cos28°. Horizontal dimension of 39.3cm is obtained by measuring beam size of 34.7cm.

*l*is the horizontal length of the test part, θ is the incident angle, n

_{0}is the refractive index. Better than 91 percent can be obtained in our measurement. The ratio of thickness to size

*d*/

*l*is less, the measurable percent is larger. If the part is used in laser facility at the same angle as being measured, the loss section can be omitted.

## 4. Verification of the inhomogeneity result

5. J. Schwider, R. Burow, K.-E. Elssner, R. Spolaczyk, and J. Grzanna, “Homogeneity testing by phase sampling interferometry,” Appl. Opt. **24**(18), 3059–3061 (1985). [CrossRef] [PubMed]

10. D. M. Aikens, “Origin and evolution of the optics specifications for the National Ignition Facility,” Proc. SPIE **2536**, 2–12 (1995). [CrossRef]

^{−5}(PV). The inhomogeneity RMS is 1.7 × 10

^{−6}. The repeatability of normal incidence is evaluated by the accuracy of the wavefront measurement [[11]]. The meaning of 5 nm wavefront accuracy is 1 × 10

^{−7}if the sample is 50 mm thick. It is the same order as the oblique measurement repeatability.

^{−5}(PV) and 1.88 × 10

^{−6}(RMS) for ease of comparison. The inhomogeneity difference between the results measured at different incidences, e.g. Figure 4 and corrected Fig. 6, is 7 × 10

^{−7}(PV) and 4.4 × 10

^{−7}(RMS). When the aperture is selected to be 350mm × 400mm (normal inciedence) shown as Fig. 8, e.g. 309mm × 400mm shown as Fig. 9 (oblique-incidence), the inhomogeneity difference is decreased. The wavefront map is inhomogeneity map multiplied by depth d. The result of Fig. 8 has been corrected by dividing cosθ′. The cross profiles at the same reference point are shown on the right side of the Figs. 8 and 9. The up curve is the wavefront profile at x-line and the down curve is the wavefront profile at y-line. The x-line wavefront PV is displayed at below. The two x-lines of Fig. 8 and Fig. 9 are similar. The difference of PV values is 1.33nm between 220.59nm and 219.26nm which is corresponded to 2.4 × 10

^{−7}of inhomogeneity PV.

## 5. Conclusion

_{1}, T

_{2}, reflectance A and B are used for deducing the inhomogeneity profile of the sample at oblique incidence. The repeatability of the results is 1.4 × 10

^{−7}. The reliability is verified by comparing with the result measured at normal incidence.

## Acknowledgment

## References and links

1. | J. H. Campbell, R. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. Whitman, J. Yu, M. Runkel, M. Riley, M. Feit, and R. Hackel, “NIF Optical materials and fabrication technologies: an overview,” Proc. SPIE |

2. | W. H. Williams, “NIF Large optics metrology software: description and algorithms,” UCRL-MA-137950-REV-1(2002). |

3. | F. Twyman and J. W. Perry, “The determination of Poisson’s ratio and of the absolute stress-variation of refractive index,” Proc. Phys. Soc. Lond. |

4. | F. E. Roberts and P. Langenbeck, “Homogeneity evaluation of very large disks,” Appl. Opt. |

5. | J. Schwider, R. Burow, K.-E. Elssner, R. Spolaczyk, and J. Grzanna, “Homogeneity testing by phase sampling interferometry,” Appl. Opt. |

6. | L. L. Deck, “Multiple surface phase shifting interferometry,” Proc. SPIE |

7. | J. Park, L. Chen, Q. Wang, and U. Griesmann, “Modified Roberts-Langenbeck test for measuring thickness and refractive index variation of silicon wafers,” Opt. Express |

8. | D. Schönfeld, T. Reuter, R. Takke, and S. Thomas, “Stitching oil-on interferometry of large fused silica blanks,” Proc. SPIE |

9. | R. Jedamzik, J. Hengst, F. Elsmann, C. Lemke, T. Döhring, and P. Hartmann, “Optical materials for astronomy from SCHOTT: the quality of large components,” Proc. SPIE |

10. | D. M. Aikens, “Origin and evolution of the optics specifications for the National Ignition Facility,” Proc. SPIE |

11. | SCHOTT Technical Information: TIE-26 - Homogeneity of optical glass, 6 (2004). |

**OCIS Codes**

(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(120.4630) Instrumentation, measurement, and metrology : Optical inspection

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: June 3, 2013

Revised Manuscript: August 12, 2013

Manuscript Accepted: August 20, 2013

Published: August 28, 2013

**Citation**

Luan Zhu, "Inhomogeneity measurement at oblique incidence by phase measuring interferometers," Opt. Express **21**, 20730-20737 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-18-20730

Sort: Year | Journal | Reset

### References

- J. H. Campbell, R. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. Whitman, J. Yu, M. Runkel, M. Riley, M. Feit, and R. Hackel, “NIF Optical materials and fabrication technologies: an overview,” Proc. SPIE5341, 84–101 (2004). [CrossRef]
- W. H. Williams, “NIF Large optics metrology software: description and algorithms,” UCRL-MA-137950-REV-1(2002).
- F. Twyman and J. W. Perry, “The determination of Poisson’s ratio and of the absolute stress-variation of refractive index,” Proc. Phys. Soc. Lond.34(1), 151–154 (1921). [CrossRef]
- F. E. Roberts and P. Langenbeck, “Homogeneity evaluation of very large disks,” Appl. Opt.8(11), 2311–2314 (1969). [CrossRef] [PubMed]
- J. Schwider, R. Burow, K.-E. Elssner, R. Spolaczyk, and J. Grzanna, “Homogeneity testing by phase sampling interferometry,” Appl. Opt.24(18), 3059–3061 (1985). [CrossRef] [PubMed]
- L. L. Deck, “Multiple surface phase shifting interferometry,” Proc. SPIE4451, 424–431 (2001). [CrossRef]
- J. Park, L. Chen, Q. Wang, and U. Griesmann, “Modified Roberts-Langenbeck test for measuring thickness and refractive index variation of silicon wafers,” Opt. Express20(18), 20078–20089 (2012). [CrossRef] [PubMed]
- D. Schönfeld, T. Reuter, R. Takke, and S. Thomas, “Stitching oil-on interferometry of large fused silica blanks,” Proc. SPIE5965, 59650V, 59650V-8 (2005). [CrossRef]
- R. Jedamzik, J. Hengst, F. Elsmann, C. Lemke, T. Döhring, and P. Hartmann, “Optical materials for astronomy from SCHOTT: the quality of large components,” Proc. SPIE7018, 70180O, 70180O-10 (2008). [CrossRef]
- D. M. Aikens, “Origin and evolution of the optics specifications for the National Ignition Facility,” Proc. SPIE2536, 2–12 (1995). [CrossRef]
- SCHOTT Technical Information: TIE-26 - Homogeneity of optical glass, 6 (2004).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.