Reimaging Lens Polarization

1
As-Built Performance of the FPP
Spectro-Polarimeter October, 2004 FPP Team
Bruce W. Lites 303 497 1517 lites_at_ucar.edu
2
FPP Spectro-Polarimeter Performance

• AS-BUILT PERFORMANCE OF THE FPP-SP
• Slit Scanning mechanism
• Vignetting as the image is scanned across the
  slit
• Spectral response function
• Signal/Noise (polarimetric precision)
• Scattered Light
• System Polarization Calibration

3
Performance Requirements

• Polarization Accuracy Matrix (for measured Stokes
  parameters I,Q,U,V)
• Spectrum Range 6301-6303 Å
• Spectral Purity FWHM ? 35 mÅ
• Spectral Sample ? 25 mÅ
• Undispersed light scatter lt 0.01
• Polarization signal-to-noise, continuum gt 10001

4
Performance of the Slit Scanning Mechanism

• In order to produce maps of the vector magnetic
  field, the slit scanner should provide regular
  and reproducible samples of the image plane in
  the direction perpendicular to the slit.
• The slit scanning mechanism nominal range is 2000
  steps of 0.16 arcsec on the Sun
• Requirements
• Repeatability 0.33 step
• Linearity no two adjacent steps separated by gt
  0.32 arcsec
• Performance
• Step size on Sun 0.148 arcsec (average)
• Range to limit switches 3233 steps (478.9 arcsec
  on Sun only 320 arcsec are needed)

5
Theodolite Measurements of Slit Scanner
Measured deflection of the beam as a function of
slit scan step number. Also shown is the linear
fit to the points. (Scan mirror motion of 1
arcsec corrseponds to 1/13.3 arcsec motion of the
solar image on the slit)
Departures of the measured beam deflection are
shown as a function of scan mirror step position.
A periodic error in the deflection corresponds
to one rotation of the ball screw. Amplitude of
this error is of order 1.2 arcsec on the sun per
400 steps (60 arcsec of scanning)
6
Theodolite Measurements of Slit Scanner
Repeatability of the scanner is measured for 4
short scans around the center of the slit scan
range. Measured positions agree within 1
arcsec, corresponding to 0.075 arcsec on the
Sun. Some of this error may arise from the
measurement process.
7
Optical Verification of Slit Scanner In Completed
FPP

Map of reticle image test central range of slit
scanner
8
Optical Verification of Slit Scanner In Completed
FPP

Deviation of measured reticle line from a linear
fit
black steep slope line red shallow slope line
9
Slit Scanner Performance

• Large-scale sinusoidal variations in the slit
  scan step size 1.2 arcsec deviation from linear
  over 400 steps (60 arcsec)
• Short scans positions are repeatable within
  about 0.15 arcsec peak (0.025 arcsec rms)
• No adjacent steps deviate by more than 1 step

10
Slit Scan Vignetting
Scan Mirror Step Number
Scan Mirror Step Number
19 August 2004 NAOJ SP intensity vs. scan mirror
position before pre-slit repair. FPP on OBU with
solar feed.
26 May 2005 NAOJ SP intensity vs. scan mirror
position after pre-slit repair. FPP on optical
bench. Solar feed with telescope simulator.
11
FPP-SP Spectral Resolution

• Spectral resolution was monitored by measurement
  of the spectrum from the tunable laser
• Rotating diffuser in beam to reduce laser speckle
• Short integrations to minimize the effects of
  drift of the laser wavelength
• Image at right shows sample laser measurement in
  both polarization images
• Tuning the laser wavelength allows measurement of
  spectral response over the entire image plane

12
FPP-SP Spectral Resolution

• Fitted Laser Line Width Along Slit Periodic
  Width Variation
• Spectrum is undersampled (instrumental width
  is25mÅ, sampling is 21.3mÅ)
• Spectrum curvature samples the profile along the
  slit at differing shifts relative to the peak of
  the emission line
• Gaussian fitting procedure has some sensitivity
  to phase of undersampled points relative to the
  emission line center

13
FPP-SP Spectral Resolution

• Measured Variation of Spectral Resolution along
  Slit Length and Within Spectral Field of Each
  CCDSIDE
• Post-vibration data, 8 February 2006
• Average spectral width in 100-pixel bins along
  slit
• No significant variations either along the slit,
  or as a function of wavelength
• All widths considerably smaller than 35mÅ
  requirement

14
FPP-SP Spectral Resolution
Use the Spectrum Curvature to Advantage

• Assume small variation of the spectral resolution
  profile along the length of the slit
• Normalize each spectral profile
• Shift each profile to a common line center
  position (shift from fitting procedure)
• Arrive at an instrumental resolution profile
  highly sampled in wavelength
• Red wing asymmetry a feature of the spectrograph
  design

15
FPP-SP Polarization S/N

• FPP-SP flux levels measured during Sun tests
• Measurements of transmission of heliostat and
  window
• Solar radiance measurements simultaneously during
  Sun tests
• Radiance measurements calibrated to zero airmass
• These measurements and extrapolations allow one
  to extrapolate to the on-orbit S/N in
  polarimetric measurements

• Inputs
• Dark-corrected continuum intensity in raw
  measurement units (DN)
• Measured SP CCD scale factor 100 e-/DN
• Read Noise 110 e-
• Heliostat transmission at 630 nm 0.51
• Atmospheric transmission at time of measurements
  0.58
• Sum two sides of CCD
• Polarization modulation efficiency 0.5
• Anticipated S/N, Typical 4.8 sec Integration
• Continuum, Quiet Sun 1100
• Line center, Quiet Sun 580
• Line center, Umbra 164

16
Scattered/Stray Light in the FPP-SP

• Measurements made of scattering inside the
  spectrograph by means of a mask placed over the
  slit.
• Intensity as a function of distance from the mask
  edge shows
• Maximum intensity adjacent to the mask edge is
  0.017 of the illuminated intensity
• Scattering falls below the required 10-2 level
  at a distance of 60 pixels (10 arcsec) from the
  edge

17
FPP-SP Polarization Calibration

• Calibration of entire SOT-FPP-SP optical system
  during Sun tests, June 2005
• Linear, right-, and left-circular polarizers over
  entrance of OTA

• Observations
• Clear (no polarizer)
• Linear, right-, left-circular polarizers
• Four rotation stations of each 0º, 45º, 90º,
  135º
• Standard mode observations (4.8s integrations)
• Two spectral ROIs covering entire spectral range
• Nine such data sets covering entire slit scan
  range

18
FPP-SP Polarization Calibration

• Data Analysis
• Bin data spatially along slit (16x) and
  spectrally (2x) to reduce data volume and
  increase S/N
• Normalize each Stokes vector observation to the
  measured Stokes I
• Each binned pixel for each CCDSIDE was subjected
  to a non-linear least-squares fitting procedure
  to determine
• 15 polarization response matrix elements (0,0
  element I?I crosstalk set to unity)
• Mount offset error of angular orientation for
  right- and for left-circular polarizers

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FPP-SP Polarization Calibration
Polarization Accuracy Requirement and Measured
Polarization Response Matrix
1.00000 0.21996 0.01587 0.00437
-0.00033 0.48083 0.07739 -0.00125
-0.00072 0.06002 -0.47494 -0.00561
-0.00028 0.00437 -0.00792 0.52939
Typical system response matrix for CCDSIDE0, for
the left ROI (without strong spectral lines).
Off-diagonal values highlighted in red exceed
those of the polarization accuracy matrix.
Polarization Accuracy Matrix Requirement

• It is almost the case that no polarization
  calibration is necessary response matrix is
  nearly diagonal, within the required accuracy!
• Calibration should improve the polarization
  precision by at least an order of magnitude
  better than the requirement

20
FPP-SP Polarization Calibration
Features of the polarization response matrix
1.00000 0.21996 0.01587 0.00437
-0.00033 0.48083 0.07739 -0.00125
-0.00072 0.06002 -0.47494 -0.00561
-0.00028 0.00437 -0.00792 0.52939
Typical system response matrix for CCDSIDE0, for
the left ROI (without strong spectral lines).
Off-diagonal values highlighted in red exceed
those of the polarization accuracy matrix.
Polarization Accuracy Matrix Requirement

• The off-diagonal Q?U and U?Q elements (in red)
  represent a simple rotation of coordinate system,
  in this case by only about 2.5º.
• The second element of the first row shows the
  large value of Q?I crosstalk typical of a
  single-beam polarimeter. When the two CCDSIDEs
  are combined, this response is largely cancelled.
• Diagonal elements are close to their anticipated
  values.
• Intensity to polarization crosstalk (first column
  of the matrix) is very small.

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FPP-SP Polarization Calibration
Spatial/Spectral Variation of the Measured
Polarization Response Matrix
ROI 0-112
ROI 112-224

• Variations of the matrix across the field are
  smaller than the uncertainties, except for first
  column (I?Q,U,V, easily calibrated on orbit)
• Residual smoothed variations are on the order of
  few x 10-4 of the continuum intensity

----- 0.00040 0.00053 0.00037 0.00432
0.00308 0.00115 0.00077 0.00173 0.00139
0.00289 0.00130 0.00203 0.00045 0.00035
0.00166
RMS fluctuations of the response matrix for ROI
0-112, CCDSIDE0
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FPP Spectro-Polarimeter Performance

• SUMMARY
• The FPP-SP meets (and exceeds) its performance
  requirements
• Polarization calibration will be carried out as a
  function of wavelength, dimension along the slit,
  and slit scan position to account for small
  variations
• The spectral response function, highly sampled in
  wavelength, will be used in the inversion process
• Signal/Noise is higher than anticipated because
  of excess read noise in the cameras.
  Nonetheless, the goal of 10001 in the continuum
  per spectral/spatial pixel is achieved