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Effect of non-uniformity of PEM retardance …

File: WGP presentation october 3 expanded.pdf

Effect of Non-Uniformity of Retardance Imposed by Photoelastic Modulators on Polarization Angle Measurements by MSE

• S. Scott, J. Ko, R. Granetz

DNB Meeting October 3, 2005 Expanded Edition (October 5, 2005)

Motivation

• The maximum retardance imposed by a photoelastic modulator is a

function of position across the crystal surface.

• Most MSE systems use only the center of the PEM, so as to get a

constant retardance for all rays.

• The C-Mod MSE system uses much more of the PEM surface, due

to other constraints in the optical design.

• We see changes in the measured polarization direction as a small

light source is moved around, within the nominal viewing area of an MSE channel on C-Mod.

• Are these changes caused by variations in the retardance imposed

by the PEMs?

Motivation

• The maximum retardance imposed by a photoelastic modulator is a

function of position across the crystal surface.

• Most MSE systems use only the center of the PEM, so as to get a

constant retardance for all rays.

• The C-Mod MSE system uses much more of the PEM surface, due

to other constraints in the optical design.

• We see changes in the measured polarization direction as a small

light source is moved around, within the nominal viewing area of an MSE channel on C-Mod.

• Are these changes caused by variations in the retardance imposed

by the PEMs?

fan cardboard shroud circular LED array diffuser mask with 4mm hole MSE Lens L1 wire grid polarizer Optical table along DNB trajectory alignment target (removed during angle measurements)

support moves left, right and up, down to position spot of light

Configuration: scans 20 and 21

* Average of 0.70, 0.72 ** Average of 0.26, 0.30, 0.30 *** Average of 0.12, 0.18

Change in Measured Polarization Angle (MSE frame) using Wire Grid Polarizer

Channel 0: MSE scan 20, shots 1050928100-113 (analysis try 2) standard deviation = 0.35o. Channel 4: MSE scan 21, shots 1050928114-117, 128-134, 136-139 (analysis try 2) standard deviation = 0.17o. Signal strength for “edge” spots (positions b and d) is lower than “central” spots by factor 4-5. Measurement precision for channel 0 is about 0.015o for “c” position and 0.03o for “b/d” positions. Angle differences are defined relative to position 4c. Actual values for 4c = -6.19o (channel 0) and

• 4.99o (channel 4).

0.28 0.71* 0.91 0.31

• 0.43
• 0.06

0.16 0.06 0.40 0.36 0.00 0.26

Channel 0

0.29**

0.15***

0.11 0.43

• 0.13

0.11 0.40 0.25 0.03 0.26 0.0

• Channel 4

1b 1c 1d 6b 6d 2c 6c 5c 3c 4b 4c 4d Spot Positions

fan cardboard shroud circular LED array diffuser mask with 4mm hole MSE Lens L1 alignment target (removed during angle measurements)

support moves left, right and up, down to position spot of light

Configuration: scan 30

Optical table along DNB trajectory precision linear polarizer

Scan 30: Measured Angle in Channel 0 is a Smooth & Reproducible Function of Spot Position of Masked Light Source

LOCUS: sds11 105 110 115 120 125

shot-1050929000.

• 1.2
• 1.0
• 0.8
• 0.6
• 0.4
• 0.2

0.0

same position same position

Measured Angle (pa_0) Note: small left-right effect.

Ray Tracing Indicates that Light from Different Spots within Viewing Area of Channel 0 Intersects PEMs at Different Positions

Median: -6.2, -3.3 mm Median: -7.7, -4.3 mm Median: -3.8, -8.1 mm Median: -2.7, -6.8 mm Upper Left (PEM-1) Upper Right Lower Right Lower Left Courtesy: J. Ko

Ray Tracing Also Shows Variations in Position of Optical Rays at PEM-2

Median: -9.4, -4.6 mm Median: -5.8, -11.6 mm Median: -4.2, -9.9 mm Median: -11.3, -6.1 mm Upper Left (PEM-2) Upper Right Lower Right Lower Left Courtesy: J. Ko

Position on PEM affects Maximum Imposed Retardance Retardance Affects Measured Polarization Angle

• Retardance is quadratic along one PEM axis, and independent of position along

the other axis.

• tan (2γ) = Jo(Ao) A40 / Jo(Bo) A44.
• Assuming that the quadratic axis is the second dimension in the median values

computed in the previous plots, the expected change in angle among the four spot positions is 1.4 degrees … in good agreement with the measured differences.

• So we expect variations of order a degree in the measured polarization

direction for light emitted from various spots within the viewing area of channel 0.

• The effect on polarization measurements that use the whole viewing area will

be considerably smaller, due to averaging.

• Variations will be caused by changes in the (mostly vertical) intensity distribution

within the viewing area of a channel, e.g. shot-to-shot, or beam-into-gas vs LED.

• My guesstimate: averaging will reduce this effect by 1-2 orders of magnitude

for beam-into-gas versus beam-into-plasma.

Are Observed Changes in Measured Polarization Angle Consistent with Inferred Changes in Retardance?

• Yuh (Ph.D. disseratation, p. 125-126) shows that we can infer the actual

retardance of PEM-1 and PEM-2 from particular ratios of FFT amplitudes:

– A38/A42 = function(Ao = PEM-1 retardance) – A46/A42 = function(Bo = PEM-2 retardance)

• Knowing Ao and Bo, we can predict the change in observed polarization

angle:

– tan (2 γ) = J2(Ao) A40 / J2(Bo) A44

• Defining A40/A44 = 1, we can evaluate the expected measured angle given

Ao and Bo. This provides a measurement of the effect of angle due to changes in retardance in PEM-1 and PEM-2.

• Question: does the computed changes in angle equal the measured

changes in angle?

Scan 30: FFT Amplitudes at 38, 42, 46 kHz Provide Measurement of Effective Retardance for PEM-1 and PEM-2

FFT scan 30 ch0 1050929109-124

2 4 6 8 10 12 Shot index 0.000 0.002 0.004 0.006 0.008 0.010 Amplitude a42 a38 a46

Scan 30: Ratio of Bessel Function J2 Evaluated at Inferred Retardances for PEM-1 and PEM-2

Scan 30 ch 0 1050929109-124 FFT ratios

2 4 6 8 10 12 Shot index 0.0 0.1 0.2 0.3 0.4 0.5 0.6

A38/A42 A46/A42

Scan 30: Effective Retardance for PEM-1 and PEM-2 Inferred from FFT amplitudes at 38, 42, 46 kHz

Scan 30 ch0 1050929109-124 PEM retardance

2 4 6 8 10 12 Shot index 2.2 2.4 2.6 2.8 PEM-1 PEM-2

Scan 30: Bessel Function J2 Evaluated at Inferred Retardance for PEM-1 and PEM-2

2 4 6 8 10 12 Shot index 0.40 0.42 0.44 0.46 0.48 0.50 J2(Ao) J2(Bo)

Scan 30: Ratio of Bessel Function J2 Evaluated at Inferred Retardances for PEM-1 and PEM-2

Scan30 ch0 J2(A_o)/J2(B_o)

2 4 6 8 10 12 Shot index 1.00 1.02 1.04 1.06 1.08 1.10

Except for Shots with Low FFT Intensity, the Predicted Changes in Measured Polarization Angles, based on Inferred Retardance

• f PEMs, is Smaller than Observed Changes

Scan 30 0.5*atan(J2(A_o)/J2(B_o))

2 4 6 8 10 12 Shot index 22.4 22.6 22.8 23.0 23.2 23.4 23.6 Degrees

Conclusions

• We see variations of ~1.2 degrees as a small light source is moved around,

within the nominal field-of-view of MSE channel 0.

– Variations are seemingly random when the WGP is used to create polarized light. – Variations are systematic (up/down) when a fixed polarizer at the DNB is used to create polarized light.

• Ray tracing indicates that optical rays strike PEM-1 and PEM-2 across a

wide region, not just at the center.

• Semi-quantitatively, the expected change in retardance due to changes in

the location of rays at PEM-1 and PEM-2 would account for the observed changes in measured angle.

• But, when we actually measure the PEM retardance, the changes are too

small to account for the observed changes in measured angle.

Speculation

• Is it possible that Howard’s method of inferring the PEM retardance

is flawed and that it underestimates actual changes in retardance?

• If so, then our observation of ‘small’ changes in PEM retardance

between in-vessel, beam-into-gas and beam-into-plasma configurations might be in error.

• So possibly, could the PEMs be responsible for our calibration

difficulties?