Abstract

The multi-pass solution for surface measurements with the help of a Shack-Hartmann sensor (SHS) on the basis of a Fizeau cavity enables fast access to surface deviation data due to the high speed of the SHS and easy referencing of the measured data through difference measurements. The multi-pass solution described in a previous publication [J. Schwider, Opt. Express 16, 362 (2008)], provides highly sensitive measurements of small displacements caused by thermal non-equilibrium states of the test set up. Here, we want to demonstrate how a pulsed thermal load changes the surface geometry. In addition the temporal response for different plate materials is monitored through a fast wave front measurement with very high sensitivity. The thermal load close to a delta-function in time will be applied from the back-side of a plane plate by heating a small Peltier element with a heat impulse of known order of magnitude. The development of the surface deviation on the time axis can be monitored by storing a set of successive deviation pictures.

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References

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  1. G. Schulz, and J. Schwider, Interferometric testing of smooth surfaces, Progress in Optics, E. Wolf, ed., (Elsevier Publisher New York, 1976) Vol. 13.
  2. J. Schwider, “Fizeau-type multi-pass Shack-Hartmann-Test,” Opt. Express 16(1), 362–372 (2008).
    [CrossRef] [PubMed]
  3. R. Bünnagel and Z. Angew, Phys. 8, 342 (1956); Opt. Acta (London); 3, 81 (1956); Z. Instrumentenk . 73, 214 (1965).
  4. J. Hartmann, “Objektivuntersuchungen,” Ztschr. für Instrumentenkunde 24 erstes Heft 1–21; zweites Heft 3–47; viertes Heft 97–117 (1904).
  5. B. Platt and R. Shack, “Lenticular Hartmann screen,” Opt. Sci. Cent. Newsl. 5, 15 (1971).
  6. D. Malacara, Optical shop testing, 3rd. Edition, (J. Wiley and Sons Inc., Hoboken, New Jersey, 2007).
  7. J. Pfund, N. Lindlein, and J. Schwider, “Dynamic range expansion of a Shack-Hartmann sensor by use of a modified unwrapping algorithm,” Opt. Lett. 23(13), 995–997 (1998).
    [CrossRef]
  8. J. Schwider, “Multiple beam Fizeau interferometer with filtered frequency comb illumination,” Opt. Commun. 282(16), 3308–3324 (2009).
    [CrossRef]
  9. F. Hund, Theoretische Physik, (Teubner Stuttgart, (1966) Vol. III.
  10. A. Sommerfeld, “Partielle Differentialgleichungen der Physik,” Vorlesungen über theoretische Physik, Band VI, Verlag Harry Deutsch, Thun Frankfurt (1992).
  11. J. Pfund, private communication (2009).
  12. B. Edlen, “The refractive index of air,” Metrologia 2(2), 71–80 (1966).
    [CrossRef]

2009 (1)

J. Schwider, “Multiple beam Fizeau interferometer with filtered frequency comb illumination,” Opt. Commun. 282(16), 3308–3324 (2009).
[CrossRef]

2008 (1)

1998 (1)

1971 (1)

B. Platt and R. Shack, “Lenticular Hartmann screen,” Opt. Sci. Cent. Newsl. 5, 15 (1971).

1966 (1)

B. Edlen, “The refractive index of air,” Metrologia 2(2), 71–80 (1966).
[CrossRef]

Edlen, B.

B. Edlen, “The refractive index of air,” Metrologia 2(2), 71–80 (1966).
[CrossRef]

Lindlein, N.

Pfund, J.

Platt, B.

B. Platt and R. Shack, “Lenticular Hartmann screen,” Opt. Sci. Cent. Newsl. 5, 15 (1971).

Schwider, J.

Shack, R.

B. Platt and R. Shack, “Lenticular Hartmann screen,” Opt. Sci. Cent. Newsl. 5, 15 (1971).

Metrologia (1)

B. Edlen, “The refractive index of air,” Metrologia 2(2), 71–80 (1966).
[CrossRef]

Opt. Commun. (1)

J. Schwider, “Multiple beam Fizeau interferometer with filtered frequency comb illumination,” Opt. Commun. 282(16), 3308–3324 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Opt. Sci. Cent. Newsl. (1)

B. Platt and R. Shack, “Lenticular Hartmann screen,” Opt. Sci. Cent. Newsl. 5, 15 (1971).

Other (7)

D. Malacara, Optical shop testing, 3rd. Edition, (J. Wiley and Sons Inc., Hoboken, New Jersey, 2007).

R. Bünnagel and Z. Angew, Phys. 8, 342 (1956); Opt. Acta (London); 3, 81 (1956); Z. Instrumentenk . 73, 214 (1965).

J. Hartmann, “Objektivuntersuchungen,” Ztschr. für Instrumentenkunde 24 erstes Heft 1–21; zweites Heft 3–47; viertes Heft 97–117 (1904).

F. Hund, Theoretische Physik, (Teubner Stuttgart, (1966) Vol. III.

A. Sommerfeld, “Partielle Differentialgleichungen der Physik,” Vorlesungen über theoretische Physik, Band VI, Verlag Harry Deutsch, Thun Frankfurt (1992).

J. Pfund, private communication (2009).

G. Schulz, and J. Schwider, Interferometric testing of smooth surfaces, Progress in Optics, E. Wolf, ed., (Elsevier Publisher New York, 1976) Vol. 13.

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Figures (9)

Fig. 1
Fig. 1

Multi-pass Fizeau with SH sensor for thermal stress monitoring.

Fig. 2
Fig. 2

Parasitic reflections caused by the reflected light arrangement of two highly reflecting Fizeau plates. Reflections 1 and 2 will always contribute to parasitic light because they are reflected from curved surfaces of the collimator. Reflections 3 and 4 are added due to the high reflectivity of the Fizeau plates which are equivalent in their intensity with 1, 2 in forward direction. On the right: an overview over the reflex chain from an actual Fizeau resonator is given (reflectivity of the Fizeau plates: R>95%, p: number of passes through Fizeau resonator).

Fig. 3
Fig. 3

Disturbances caused by the reflected light arrangement. Above (spatial filter removed): 3a: disturbances together with spots from the different passes, 3b: Fizeau obstructed (only contribution from collimator lens); 3c: Fizeau cavity being obstructed through a screen between plates. Below (spatial filter inserted): 3d: Fizeau obstructed (only contribution from collimator lens); 3e: Fizeau cavity obstructed through screen between plates.

Fig. 4
Fig. 4

Repeatability (wave aberrations) measurement run without multi-pass (Mean values: PV = λ/67, RMS = λ/357; λ = 532nm).

Fig. 5
Fig. 5

Repeatability (wave aberrations) measurement with multi-pass p = 30 (Mean values for the wave aberrations as seen by the SHS: PV = λ/14, RMS = λ/100; λ = 532nm.

Fig. 6
Fig. 6

Time response of a BK7 plate exposed to heating. Measured wave aberrations enhanced through a multi-pass resonator, number of passes: p = 25, He-Ne-Laser (λ = 543nm). First row (a_1): aberration before heating, first row (b_1): Maximum value of aberration after ca. 20 sec heating (contour line distance: 0,5 waves), second row (a_2 &b_2): pseudo-3D-plots of the aberrations of first row. Third row (c_1): Intermediate state showing a buckling due to the heat flow along the plate normal in combination with an optical path difference caused by heating the air gap between the Fizeau plates, third row (d_1): State of the deformation after 380 sec, fourth row (c_2&d_2): pseudo-3D-plots of deviations of third row. Please note the change of the contour line distances in the different contour line plots!

Fig. 7
Fig. 7

Time response given as wave aberrations of a BK7-plate: 60mm diameter, 12mm thick, heating period ca. 10 sec, starting after 15 sec, p = 25, Maximum of surface deformation of BK7 plate: 87nm, PV-values greater than RMS-values! Thermal expansion coefficient: 7,1-8,3 10−6/K

Fig. 8
Fig. 8

Time response given as wave aberrations of a fused silica, plate diameter: 60mm, 12mm thick, heating period 20 sec, p = 30, Maximum of surface deformation of silica-plate:4,9 nm, PV-values greater than RMS-values! Thermal expansion coefficient: 0,54 10−6/K.

Fig. 9
Fig. 9

Aberrations measured with a multi-pass factor p = 30 using a He-Ne-Laser (λ = 543nm) Fused silica plates, heating period about 10 sec., above (a_1&a_2): start aberration, middle (b_1&b_2): maximum aberrations due to bending after 78 sec, below (c_1&c_2): state after 128 sec (Please note the change of the contour line distance from row to row!).

Tables (1)

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Table 1 Global rating is always an awkward business. Here it has been undertaken to compare two optical test methods employing the Fizeau measuring philosophy known primarily from interferometry. The main idea is that the referencing is done with the help of a reference mirror being part of a Fizeau resonator. The most influential distinction results from the fact that the SH-test can only make the referencing in time succession, and in contrast to this, the Fizeau interferometer provides the reference at the same time.

Equations (3)

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Δ W ( u ) = 2 z 2 z cos u z u 2 ,
T ( r , t ) 1 t 3 T ( r , 0 ) e ( r r ) 2 4 λ t d r ,
T ( r , t ) 1 t 3 e r 2 4 λ t .

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