OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 18 — Sep. 9, 2013
  • pp: 20730–20737
« Show journal navigation

Inhomogeneity measurement at oblique incidence by phase measuring interferometers

Luan Zhu  »View Author Affiliations


Optics Express, Vol. 21, Issue 18, pp. 20730-20737 (2013)
http://dx.doi.org/10.1364/OE.21.020730


View Full Text Article

Acrobat PDF (1613 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

The huge power solid-state lasers contains many large rectangular optical glass over 600 mm such as the laser of National Ignition Facility and the Laser of Megajoule etc [1

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]

]. The quality of the optics is specified over the full aperture [2

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

]. The refractive index inhomogeneity of these large blanks used for these facilities has to be measured.

Inhomogeneity is a measurement of the variation in the refractive index within a material. Inhomogeneity is tested by phase measuring interferometer including a number of techniques. A well-known four-step method is developed by Twyman and Perry [3

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]

], Roberts and Langenbeck [4

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

] and Schwider [5

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]

]. The refractive index inhomogeneity is evaluated by four interferometer’s measurements. The glass sample is polished for suppressing surface irregularities and a small wedge must be applied to the sample. A linear gradient of refractive index cannot be detected in this method. The linear gradient of refractive index of a parallel plate can be measured with Fourier Transform Phase-Shifting Interferometry (FTPSI) due to the simultaneous measurement of the surface profiles during a single wavelength scan [6

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

]. A alternative simple method is given by Schwider using a two-step procedure with the glass sample or not where the glass plates are connected with the samples using an immersion oil liquid that has the same refractive index as sample [5

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]

]. The sample does not need to be polished for the measurement. Other improvement is described that four-step method is simplified to three steps by directly measuring the interference between the front and back surface instead of two measurements [7

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]

]. To our knowledge all the measurements are measured at normal incident angle. Therefore the size of measurements is limited to the interferometer aperture.

There are two methods to attain the inhomogeneity of full size over the instrument aperture. Stitching is well known method for enlarging the size in measuring wavefront profile. It is adapted to measure the inhomogeneity of large blanks with oil-on measurement [8

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

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]

]. Positioning inaccuracy and the algorithm is the main error source for the stitching. Another method is extrapolating which it is only suitable for some special case. The large blanks are measured on two parts, then the power and astigmatism of the inhomogeneity over the full aperture is extrapolated from the half part results [2

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

]. The extrapolating equations are based on ideal mathematic models without considering the deviation of real materials.

2. Description of the method

The method is based on optical path difference measurements of the glass block in transmitted and reflected light by phase measuring interferometer. The interferometer has a Transmission Flat (TF) and a Reference Flat (RF). The test part of glass must be polished. It is suggested that the surfaces quality should be less than 5 wavelengths peak-to-valley. The polished glass must have a wedge about 10−3 rad so that the reflections from the different surfaces of sample can be separated on the detector plane.

Five measuring procedures are required for the algorithm as shown in Fig. 1
Fig. 1 Five-step procedure for inhomogeneity evaluations at oblique angle.
. For the first measurement, the wavefront of the cavity consist of TF and RF is measured. The beam passes through TF and is reflected off RF. During the second measurement, the test part is inserted at oblique incident angle θ. The beam passes through TF and the test part, and is reflected off RF. The third measurement is similar to the second one, except that the test part is rotated 2θ around vertical axis. The beam passes through TF and the test part, and is reflected off RF. In the fourth measurement, the test part is kept the state of the third step, and RF is moved and adjusted to keep the light returning back exactly. Then the beam passes through TF and is reflected off the front of the test part and RF. The fifth measurement is like the fourth measurement, and the beam through TF is reflected off the back side of the test part and RF.

n(x,y)=n0+Δn(x,y)
(1)

The wave aberrations measured in the different step of the five-step procedure are defined as C, T1, T2, A and B, respectively. The Interferogram Scale Factor of 0.5 is used during five-step measurement. Their relationships are deduced as following:
C=Z1+Z2,
(2)
T1=Z1(Za'+Zb)(n0cosθ'cosθ)+Z2Δn1dcosθ',
(3)
T2=Z1(Za+Zb)(n0cosθ'cosθ)+Z2Δn2dcosθ',
(4)
A=Z1+2Zacosθ+Z2f,
(5)
B=Z1+Za(n0cosθ'cosθ)2Zbn0cosθ'Za'(n0cosθ'cosθ)+Z2f(Δn1+Δn2)dcosθ',
(6)
where Z1 and Z2 are the surface deviations of the auxiliary mirror TF and RF, Z2f is the horizontally flipped data set of Z2, Za and Zb are the front and the back surface deviations of test part, respectively. The direction is defined in Fig. 1. Δn1 and Δn2 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; Za′ is the data set of Za with a horizontal shift of x0, and x0 is the displacement on X direction between the light input and output of the front surface of the test part in the fifth measurement. x0 is expressed as Eq. (7).

x0=2dtanθ'cosθ
(7)

The surface deviation of point O, P and Q is supposed as Za, Za′ and Zb respectively. T1, T2 and B relate to same Zb. So there is only one variable Zb shown as Eqs. (3), (4) and (6). Then inhomogeneity at direction OQ can be solved by eliminating influence of direction PQ.

The expression for oblique incidence is more complicated. Fortunately the variation of the refractive index Δn2 can be solved by eliminating the variables Z1, Z2, Z2f, Za, Za′, Zb and Δn1. It is written as following:

Δn2=[2n0cosθ'C(cosθ+n0cosθ')T1+(BAT2)(n0cosθ'cosθ)]cosθ'2dcosθ
(8)

The result Δn2 is the deviation from mean refractive index n0 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.

The variation of the refractive index is separated from the surface deformations. This method is similar as the technique used in normal incidence configuration. This five-step measurement is suitable for oblique incidence, so the measurable size is enlarged over the aperture of the interferometer horizontally.

3. Experiments and discussion

A ZYGO MST 24” interferometer is used in our experiments. The surface deviations of the auxiliary mirror TF and RF (Z1 and Z2) 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 n0 is 1.5.

The five-step measurement is implemented using the method of Fig. 1. The wavefront result of C, T1, T2, 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).
lm=lcosθ+dsinθ,
(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.

The refractive angle in glass is calculated by Snell’s law.

θ'=asin(sinθn0)
(10)

The result Δn2 is calculated from Eq. (8) by the commercial software of Zygo corp. It is also conveniently obtained using other technical computing software.

Results of C, T1, T2, A and B in five-step procedure are shown in Fig. 3
Fig. 3 Wavefront results of C (a), T1 (b), T2 (c), A (d) and B (e) from five-step measurement.
, respectively. Inhomogeneity map Δn2 calculated from Eq. (8) is shown in Fig. 4
Fig. 4 Homogeneity map Δn2 at 28 degree incidence.
, 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°.

Inhomogeneity of the block is defined as peak-to-valley value (PV). Six inhomogeneity measurements are used to calculate repeatability. The six results are list in Table 1

Table 1. Results of Inhomogeneity Measured at 28 Degree Incidence

table-icon
View This Table
. The mean of the PV is 1.43 × 10−5, 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.

When the sample is test under oblique incidence, there is loss in size. The percent of measureable size to full horizontal length is expressed as t as following:

t=1dl2sinθn02sin2θ.
(11)

Where d is the depth of the part, l is the horizontal length of the test part, θ is the incident angle, n0 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

The inhomogeneity result of oblique incidence is compared with the result of normal incidence obtained by four-step measurements [[5

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]

]]. This normal-incidence result can be corrected for angle of incidence [[10

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

]]. It is divided by cosθ′, where θ′ is refractive angle shown as Eq. (10). Four results of wavefronts are C′, T′, A′ and B′ as shown in Fig. 5
Fig. 5 Wavefront result of C′ (a), T′ (b), A′ (c), B′ (d) from four-step measurement.
, respectively. The refractive profile Δn′ is calculated using Eq. (12) and shown in Fig. 6
Fig. 6 Homogeneity map measured at normal incidence.
.

Δn'=[(n01)(B'A')n0(T'C')]/d.
(12)

The size is selected to be 39.3 cm corresponding to the size 34.7 cm of 28 degree incidence. The inhomogeneity measured at normal incidence is 1.41 × 10−5 (PV). The inhomogeneity RMS is 1.7 × 10−6. The repeatability of normal incidence is evaluated by the accuracy of the wavefront measurement [[11

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

]]. 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.

The measured zones are plotted in Fig. 7
Fig. 7 Measurement zones of the test part with (a) normal incidence (b) oblique incidence.
. The light passes through the part at different directions. The normal incidence specification is corrected to be 1.49 × 10−5 (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
Fig. 8 Wavefront map measured at normal incidence. The wavefront map is homogeneity map multiplied by depth d and divided by cosθ′. The aperture is 350mm × 400mm excluding edge influence. The right curves are wavefront profiles at sampled lines. The up curve is the wavefront profile at x-line and the down curve is the wavefront profile at y-line. The PV and rms values below the curves are corresponded to x-line.
, e.g. 309mm × 400mm shown as Fig. 9
Fig. 9 Wavefront map measured at oblique incidence. The wavefront map is homogeneity map multiplied by depth d. The aperture is 309mm × 400mm excluding edge influence. The right curves are wavefront profiles at sampled lines. The up curve is the wavefront profile at x-line and the down curve is the wavefront profile at y-line. The PV and rms values below the curves are corresponded to x-line.
(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

The measurement of the inhomogeneity at oblique incidence is presented and explained. Five-step wave aberrations measurements including cavity C, transmittance T1, T2, 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

The author gratefully acknowledges the support of the Chinese Academy of Science and the discussions with Dr. Shijie Liu and Prof. Deyan Xu.

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 5341, 84–101 (2004). [CrossRef]

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. 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]

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]

10.

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

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:  Author  |  Year  |  Journal  |  Reset  

References

  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. SPIE5341, 84–101 (2004). [CrossRef]
  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.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. SPIE4451, 424–431 (2001). [CrossRef]
  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. Express20(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. SPIE5965, 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. SPIE7018, 70180O, 70180O-10 (2008). [CrossRef]
  10. D. M. Aikens, “Origin and evolution of the optics specifications for the National Ignition Facility,” Proc. SPIE2536, 2–12 (1995). [CrossRef]
  11. 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.

CrossCheck Deposited