Etalon 1053 Measurements




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Etalon 1053 Measurements
I. History
Etalon 1053 is the medium resolution etalon for SALT PFIS. It provides the medium spectral resolution mode working with the low resolution etalon in dual-etalon mode. The required characteristics for the etalon were developed in consultation with the SALT Science Working Group and through the PDR process, with input from the vendor, ICOS, about the feasibility of the proposed specifications. The final specifications for the etalon are listed in Table 1. ICOS submitted a quotation for the system on December 12, 2001. The etalon was ordered on January 14, 2002.

Table 1 Medium Resolution Etalon Specifications


clear aperture 150 mm

surface quality λ/100 at 650 nm

finesse approximately 30 at 650 nm

reflector coating 90% ± 4% from 430 nm to 860 nm

spectral resolution 2500 at 650 nm

(implied gap) 27 microns

glass reference capacitor

outer surface AR coating <1% from 430nm to 680 nm
As with etalon 1052, discussions with ICOS about possible housing re-design added significantly to the time required to manufacture the etalon. In addition, the problems with the slipped support pad on etalon 1052 further delayed the completion of etalon 1053. The etalon was received at Rutgers on July 2, 2004.

II. Test Results

The testing equipment used for characterizing this etalon is the same as described in the report on etalon 1052. The gap of the medium resolution etalon is large compared to the range of motion of the piezo actuators, so no significant variation of the etalon’s spectral resolution is possible. We will operate the etalon near its maximum gap setting to attain the highest resolution possible. The Z axis coarse setting of the controller adopted is Zc=+2. The operating mode is named MR (medium resolution). The measured properties of the etalon are presented in Table 2.


Table 2 MR Mode Properties

Wave

FWHM

FSR

Finesse

Resolution

Gap

X offset

Y offset

(Å)

(Å)

(Å)







(μ)







4240.07

6.79

32.6

4.8

624

27.56

-30

-85

4272.69

4.87

33.0

6.8

877

27.66

-30

-85

4306.08

4.12

33.7

8.2

1045

27.51

0

-110

4340.10

3.22

34.4

10.7

1348

27.38







4374.87

2.86

35.1

12.3

1530

27.24







4410.35

2.65

35.8

13.5

1664

27.13







4446.57

2.74

36.6

13.3

1623

27.03







4483.50

2.71

37.3

13.8

1654

26.96







4521.14

2.90

38.0

13.1

1559

26.90

-15

5

4559.48

3.03

38.7

12.8

1505

26.86







4598.55

3.17

39.3

12.4

1451

26.90







4638.08

3.14

40.0

12.7

1477

26.88







4678.57

3.13

40.8

13.0

1495

26.80







4719.76

3.08

41.6

13.5

1532

26.80







4761.68

3.11

42.3

13.6

1531

26.80







4804.36

3.07

43.1

14.0

1565

26.81







4847.79

3.08

43.8

14.2

1574

26.82







4892.00

2.76

44.6

16.2

1772

26.82







4937.02

2.74

45.4

16.6

1802

26.82







4982.88

2.86

46.3

16.2

1742

26.81

-10

0

5029.63

2.91

47.2

16.2

1728

26.80







5077.26

3.05

48.1

15.8

1665

26.81







5125.77

3.51

49.0

14.0

1460

26.81







5175.25

3.17

49.9

15.8

1633

26.82







5225.65

3.21

50.9

15.9

1628

26.84







5277.01

3.21

51.8

16.2

1644

26.86







5329.34

3.21

53.1

16.5

1660

26.76







5383.15

3.11

54.1

17.4

1731

26.79







5437.51

3.12

54.9

17.6

1743

26.94







5492.90

3.19

55.9

17.5

1722

26.98

-25

5

5549.35

3.26

57.0

17.5

1702

27.00







5606.95

3.32

58.2

17.5

1689

27.02







5665.69

3.19

59.3

18.6

1776

27.05







5725.62

3.41

60.5

17.8

1679

27.08







5786.77

3.61

62.3

17.3

1603

26.87







5850.26

3.88

63.6

16.4

1508

26.92







5913.93

4.07

64.3

15.8

1453

27.19







5978.88

4.27

65.6

15.4

1400

27.25

-35

20

6045.09

4.41

66.9

15.2

1371

27.30







6112.75

4.64

68.8

14.8

1317

27.18







6182.59

4.62

69.8

15.1

1338

27.36

-60

35

6252.44

4.29

70.4

16.4

1457

27.75







6323.47

4.08

72.5

17.8

1550

27.57







6397.47

3.94

73.7

18.7

1624

27.78

-105

50

6470.82

4.13

74.8

18.1

1567

27.98







6547.11

3.94

75.9

19.3

1662

28.24







6622.62

4.21

76.0

18.1

1573

28.85

-135

70

6699.14

4.57

79.2

17.3

1466

28.35







6780.92

4.23

80.2

19.0

1603

28.65

-200

115

6859.63

4.28

79.4

18.5

1603

29.64







6939.66

4.15

81.5

19.6

1672

29.53







7022.70

4.27

83.1

19.5

1645

29.66

-230

130

7105.92

4.26

83.8

19.7

1668

30.11







7190.39

4.30

86.0

20.0

1672

30.05

-235

140

7277.95

4.35

88.8

20.4

1673

29.83







7367.93

4.33

91.3

21.1

1702

29.74







7460.51

4.45

93.9

21.1

1677

29.63







7555.77

4.71

96.1

20.4

1604

29.70

-210

125

7652.70

4.65

98.8

21.2

1646

29.64







7753.37

4.59

102.0

22.2

1689

29.46







7856.76

4.81

104.7

21.8

1633

29.47







7962.83

5.03

107.4

21.4

1583

29.52







8071.57

5.27

110.3

20.9

1532

29.52

-185

120

8183.50

5.57

113.3

20.3

1469

29.57







8298.08

5.87

116.4

19.8

1414

29.57







8416.39

6.22

120.0

19.3

1353

29.52







8538.07

6.47

123.7

19.1

1320

29.46

-190

120

8663.85

6.81

127.8

18.8

1272

29.36







8793.69

7.40

131.8

17.8

1188

29.34







8927.41

8.55

136.5

16.0

1044

29.20







9066.62

10.11

141.7

14.0

897

29.01

-180

115

9210.73

12.47

144.1

11.6

739

29.43







A. Coatings

We do not have facilities to test the reflector coatings or the AR coatings at Rutgers, and show here the curves supplied by ICOS. The high reflector coating curve (Figure 1) shows that the reflector coatings provide 90 –2.5 +2 % (peak-to peak) reflectivity over the operating wavelength range, better than the specification. The AR coatings of the outer surfaces of the plates (Figure 2) provide ≤ 1% reflectivity over most of the wavelength range, with a very minor failure to meet specification from 850 to 860 nm. We do not deem this small failure to meet specification significant, and it should not have an appreciable effect on the system efficiency.




Figure 1 High reflection coating transmission


Figure 2 Outer Plate Anti-Reflection Coating

B. Free Spectral Range


The free spectral range (FSR) is the spacing between successive transmission peaks of the Fabry-Perot. The FSR is measured by illuminating the etalon with white light, recording the transmitted spectrum, and measuring the wavelengths of the peaks. There are 66 orders in the specified operating range (430 – 860 nm) in MR mode, and 72 orders in the usable range (424 – 921 nm). The FSR measurements are presented in Table 2 above, and shown in Figure 3. In an ideal etalon, the FSR should vary as the square of the wavelength when the gap is held constant. The inflection in the FSR between 6200 and 7200 Å indicates that the effective gap changes in this region (see section C below). The curves in Figure 3 are the expected FSR of an ideal etalon for gaps of 26.8 (red curve) and 29.5 microns (green curve).
Figure 3 Free Spectral Range in MR Mode

C. Effective Gap and Parallelism

The gap between the reflecting plates is equal to λ2 / (2 FSR). The gap calculated from our measurements is listed in Table 2 and shown in Figure 4. The effective gap is nearly constant (as expected) at short wavelengths, then increases in the 600 to 710 nm range, and then is roughly constant again at a larger value at long wavelengths. The gap at 650 nm is 28.2 microns, within the 27±3 micron tolerance of the specifications. This behavior of the effective gap is very similar to that measured for etalon 1052, and arises from the design of the broad band high reflectance coatings.


Figure 4 Effective Gap in MR Mode
There is a parallelism effect related to the coating variations. The X and Y motions of the controller adjust the parallelism of the etalon plates. The optimum settings of the parallelism result in the narrowest FWHM and most symmetric spectral profiles of the etalon’s transmission. These optimum settings are listed in the “X offset” and “Y offset” columns in Table 2, and shown in Figure 5. According to ICOS’ calibration, 1 offset unit corresponds to 4.9 Å of plate motion. The character of the parallelism adjustments is the same as that of the gap variation: nearly constant at short and long wavelengths, and varying in the 6000 – 7500 Å range. The shape and amplitude of the parallelism variations for this etalon are very similar to those for etalon 1052.




Figure 5 Parallelism Settings in MR Mode


D. Plate Flatness

We have measured the shape of the etalon plates by reducing the illuminating aperture in the collimated beam to 25 mm diameter, and then measuring the peak of the transmission profile at each of seven places equally spaced along the Y axis of the etalon; we then rotate the etalon 90˚ and take the same measurements along the X axis. The measurements were made at three wavelengths in MR mode. Rotating the etalon systematically shifts the central wavelength by about 3.5 Å, possibly due to flexure in the etalon or the test set. The effective gap at each position is calculated from the measured wavelength using the relation D = n λ / 2, where D is the gap and the effective order, n, is calculated from the data in Table 2. The variation of this gap from its central value measures the plate flatness. The results are listed in Table 3 and plotted in Figure 6. It is interesting to note that although the plates were tipped by typically 500 Å in both the X and Y axes to maintain the parallelism over this wavelength range, the measured gaps agree to within ±30 Å. Thus we seem to be mostly measuring the underlying plate shape, after correcting for the coating effects. There are some coating effects, however, since the plates seem to be consistently flatter at the longest wavelength. The plates exhibit an approximately conical shape, with the gap deviations increasing roughly linearly with radius in all directions. The RMS deviation of the plates is 98.9 Å at 6550 Å, or λ/66. Weighting by the area of annular sectors, the weighted RMS deviation is 122.2 Å, or λ/54. The maximum deviation is 165 Å or λ/39. By all of these measures, the plates do not meet the flatness specification of λ/100; this larger than specified plate curvature is responsible for the lower than expected spectral resolution (see Section E below). The fwhm of the profile is narrower in these restricted apertures than averaged over the entire etalon surface, as expected with the observed large-scale departures from flatness.


Table 3 Etalon 1053 Plate Flatness

Pos.

5000

6500

8500




λ

fwhm

Δ Gap

λ

fwhm

Δ Gap

λ

fwhm

Δ Gap

(mm)

(Å)

(Å)

(Å)

(Å)

(Å)

(Å)

(Å)

(Å)

(Å)

X

-60

4983.9

1.76

-156.1

6548.9

3.35

-158.3

8419.0

6.18

-115.7

-40

4984.8

3.48

-107.7

6550.5

2.90

-88.0

8420.6

5.72

-57.5

-20

4985.8

1.65

-52.7

6551.7

3.02

-36.2

8421.7

6.29

-18.6

0

4986.8

3.54

0.0

6552.5

2.76

0.0

8422.3

5.52

0.0

20

4986.1

3.58

-36.6

6551.6

2.92

-40.1

8421.2

5.50

-37.2

40

4985.3

3.52

-76.4

6550.4

2.95

-91.9

8420.2

6.07

-73.3

60

4984.2

3.60

-138.3

6548.7

3.16

-165.2

8419.1

6.40

-112.9

Y

-60

4980.3

1.80

-174.9

6546.5

3.13

-134.6

8415.4

5.70

-88.7

-40

4981.2

3.65

-128.1

6547.4

2.83

-92.7

8416.1

5.47

-66.3

-20

4982.5

3.78

-57.6

6548.5

3.06

-44.9

8417.1

5.50

-30.9

0

4983.6

1.94

0.0

6549.6

2.81

0.0

8417.9

5.57

0.0

20

4982.8

2.03

-41.4

6548.6

3.16

-43.6

8416.9

5.48

-35.8

40

4981.9

3.65

-89.9

6547.3

2.95

-99.6

8416.0

5.50

-67.3

60

4981.2

3.76

-128.6

6545.9

3.09

-158.3

8415.4

5.55

-90.8





Figure 6 Etalon 1053 Plate Flatness


E. Spectral Resolution

When adjusted for optimum parallelism, the transmission spectral profile of the etalon is well fit by a Voigt function; Figure 7 shows a sample fit. The green curve in Figure 7 shows the fit to the data, and the red curve shows the fit with the spectrograph instrumental profile deconvolved. The (deconvolved) FWHM of the Voigt fits is listed in Table 2, and the spectral resolution (λ/FWHM) is listed there and plotted in Figure 8. The resolution at 6550 Å is 1662, less than the specification of 2500. Because of the plate non-flatness, the resolution at all wavelengths is less than desired.



Figure 7 MR Mode Spectral Profile



Figure 8 Spectral Resolution in MR Mode

F. Finesse

The finesse is the ratio of the FSR to the FWHM, and is listed in Table 2 and plotted in Figure 9. The finesse at 6550 Å is 19.3, less than the specification of 30. The expected finesse of an etalon depends on the reflectivity of the high reflection coatings and the flatness of the plates. The “reflectivity finesse” is Nr = π R1/2 / (1 – R) where R is the reflectivity; for our design reflectivity of 90%, Nr = 30. The “defect finesse” is Nd = m / 2 where m is the plate flatness in waves (λ / m). The total finesse is then N = (Nr-2 + Nd-2)-1/2. Calculating the expected finesse using the above formula with the reflectivity from Figure 1 and the weighted RMS flatness of λ/54 at 6550 Å from Section C yields the green curve in Figure 9. Treating the plate flatness parameter as a variable, and fitting to obtain the best agreement with the measured finesse curve yields a value of λ/46.4 at 6550 Å, producing the red curve in Figure 9. Neither curve fits the full range of data well, but the red curve is a better fit in the blue regions while the green curve is a better fit in the red. This may reflect the fact that the plates seem to be flatter in the red, as noted in section E above. Neither curve fits well in the region around 6100 Å, where the parallelism is changing rapidly and different regions of the aperture may have different effective parallelism requirements.


Figure 9 Finesse in MR Mode


G. Transmission

The transmission is measured by taking a spectrum through the etalon, and then sliding the etalon holder to its second position, with an identical aperture, but without the etalon, and taking another spectrum. The ratio of these spectra provides the transmission profile. The power supply to the lamp is highly regulated so the temporal variation of the source brightness is negligible; this was confirmed by repeated cycles of the above measurements. A sample transmission profile is shown in Figure 7. The measured peak transmissions at selected wavelengths are listed in Table 4. The spectrograph instrumental resolution broadens that measured profile, reducing the peak transmission. We deconvolve the instrumental profile, producing the deconvolved transmissions listed in Table 4. There are some measurements that are clearly too high, for reasons that we do not understand; small errors in the determination of the spectrograph instrumental profile cannot account for the excessively high transmissions. It is unlikely that the etalon has an actual transmission exceeding 90% at any wavelength.


Table 4 Peak Transmission

λ (Å)

Trans (%)

λ (Å)

Trans (%)

λ (Å)

Trans (%)




Meas

Deconv




Meas

Deconv




Meas

Deconv

4523

47

60

6399

80

96

7557

84

96

4893

42

55

6624

56

67

7964

64

73

5494

51

66

6781

62

73

8665

71

76

5980

66

78

7023

85

101

8754

75

79

6185

60

69

7193

89

105











H. Wavelength Calibration

The etalon is scanned in wavelength by changing the Zoffset in the controller. The scanning range (-2.048 to +2.047 in Zoffset) is sufficient to cover several free spectral ranges of the etalon. Since the change of the gap during scanning is a relatively small fraction of the gap (about 7% maximum), the spectral resolution is not significantly changed over the full scanning range. To simplify operation, we have decided to operate the etalon in the minimum number of orders (12) that will allow scanning to any wavelength within the operating range (430 – 900 nm). The results are presented in Table 5. Columns 1-4 contain the coefficients of the polynomial fit λ = A + B Zoffset + C Zoffset2 + D Zoffset3. Column 5 has the RMS scatter of the measurements about this fit. The polynomials provide excellent fits, with residuals less than 1/100 of the FWHM. We expect that the B, C and D coefficient values measured here should be very stable, but that the A coefficient value will vary with time, temperature, humidity and other environmental factors (see section I).


Table 5 Wavelength Scanning Calibration

A

B

C

D

Δλ (Å)

8891.048

159.6501

0.449058

-0.163251

0.026

8368.272

147.9848

-0.267086

0.123061

0.054

7905.325

139.1099

0.019374

0.009749

0.021

7490.323

132.3907

-0.310791

0.128880

0.044

7035.305

122.9087

-0.768342

0.265510

0.013

6624.728

119.4040

-1.011822

0.073905

0.018

6239.696

115.4225

0.839760

-0.368778

0.031

5888.902

112.1411

0.351423

-0.145437

0.030

5513.615

106.5186

-0.225120

0.069097

0.016

5182.461

101.0102

-0.328655

0.083226

0.016

4842.636

94.0644

-0.563628

0.293391

0.055

4486.035

115.0689

-3.675370

1.778911

0.073


I. Stability

We have measured the wavelength stability of the etalon by taking a series of spectra over a period of more than 24 hours. The data are presented in Table 7 and Figure 10. During these measurements the etalon and controller were undisturbed mechanically and electrically and the environmental conditions were approximately constant. The wavelength drifts were smooth and typically less than 1 Å per hour. Over the entire period of measurement, the RMS wavelength fluctuations were 0.71 Å. This drift corresponds to variation of the A calibration coefficient discussed in the previous section. Our experience with previous ICOS etalons and controllers is in good agreement with these measurements. The FWHM fluctuations over the entire period were 0.21 Å RMS.


We have also measured the stability of the parallelism settings for the etalon, over a 7 day time scale. The data are presented in Table 7. The RMS variation of the X Offset over the period was 4.1 units, and the Y Offset RMS variation was 2.4 units. Since the uncertainty of the determination of the optimum parallelism settings is about 5 units, these drifts are insignificant.

Table 7 Stability



Wavelength

Parallelism

Time (hr)

λ (Å)

FWHM (Å)

Time (days)

X Offset

Y Offset

0.00

6469.41

4.63

0.70

-90

60

0.83

6467.70

4.63

3.49

-90

55

2.00

6467.75

4.63

3.69

-90

60

3.54

6467.35

4.63

4.52

-85

55

5.39

6467.61

4.70

5.77

-85

60

7.06

6466.71

4.46

6.61

-95

60

25.06

6466.64

4.39

7.50

-95

60

26.21

6466.95

4.54










27.34

6467.33

4.76










28.51

6467.29

4.86










29.45

6467.64

5.21











Figure 10 Etalon 1053 Wavelength Stability

J. Discussion

Etalon 1053 exhibits the same bi-modal behavior of the effective gap, with its effect on parallelism, resolution, and free spectral range that we observed in Etalon 1052. There was no specification on the constancy of effective gap, and the gap is within specification at the specified wavelength of 6500 Å. The effect of the wavelength dependent parallelism setting is an annoyance and will be dealt with in the operating software, but should not degrade the performance of the system. Since a typical wavelength scan is less than 50 Å (usually much less), the operating procedure will be to set the parallelism settings to the appropriate values for the center of the scan, and there will be no need to vary the settings over the scan range. We have observed that the parallelism settings are very stable over significant time periods in the laboratory, and will investigate the stability of the parallelism settings in the SALT environment during commissioning. We suspect that they will be very stable, since it is an effect of the physical structure of the coating layers. Thus we expect that we should be able to determine the calibration of the X and Y offset settings as a function of wavelength and not need to re-determine these values each time the FP system is used.


The effective plate flatness deviates significantly from specification, reaching about the λ/50 rather than the specified the λ/100. The manufacturer has provided interferograms that indicate that the flatness of the plates met or exceeded the specifications before assembly into the etalon. We suspect that the flatness distortions may arise from effects within the multilayer high reflectance coatings. The defect finesse produced by these flatness deviations leads to lower spectral resolution and finesse than we had targeted. The spectral resolution is about 68% of the expected value of 2500. We expect that many of the science programs planned to use MR mode will still be successful at these lower resolutions, and higher spectral resolution will be provided in HR mode for those programs that need it.
The transmission of the etalons was not included in the specifications. Our PDR documentation gave a goal of 75 – 80%. The goal is generally met or exceeded in the most of the etalon’s wavelength range, but the transmission is lower, from 60 – 75%, at wavelengths shorter than 5500 Å. This is probably due to the relatively larger effect of the defect finesse at short wavelengths (a given physical distortion of the plates is a larger number of waves at shorter wavelengths).
The wavelength calibration and stability results are in agreement with our expectations based on previous FP systems. We plan on taking calibration exposures at hourly intervals during observations, and it seems that this will provide an adequate measurement of the wavelength drift of the etalon. The actual stability is likely to be heavily dependent on the environmental conditions at the telescope, so we will not be able to determine the required frequency of calibrations until commissioning at SALT.
In summary, although we are somewhat disappointed in the resolution and finesse of the etalon, we do not believe that there are any easy ways to significantly improve the performance in these areas, given the coating design of the high reflector. We recommend acceptance of the etalon and deployment in PFIS.


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