Echelle Grating Parameters

In B_12_02_17 files b022.fits to b036.fits, we took a series of gas cell exposures at different grating angles to map out the wavelength on the detector as a function of echelle voltage.  Not every file was used for mapping the echelle.  There are some with open filter that will be useful for verifying the echelon orders.

We mostly used echelle order 3 and the 18a filter, but also did a C2H2 Q-branch observation (order 4) and a long wavelength observation through the Soifer filter (order 2).  We took care to position the line we cared about so the order it was in ran through pixel (512,512) on the detector and to always move the echelle toward positive voltage before stopping.

The input parameters are (from my IDL script):

ord =  [4, 3, 3, 3, 3, 3, 3, 2, 4, 3, 3, 3]

v = [ 8.2110, 8.1983, 7.8271, 7.7745, 7.7298, 7.6508, 7.5680, 7.5680, 8.2110, 8.2975, 8.5450, 8.7121]
wn0 = [729.2440, 547.8163, 576.11451, 580.73199, 584.70852, 592.05390, 600.10351, 400.22171, 729.2440, 541.09024, 525.9599, 516.79730]

I used the C2H2 Q branch to determine that the velocity per pixel in the y-direction was 0.3793 km/s.  This corresponds to an echelon input angle of 9.88.

With the velocity per pixel, I measured the distance each line was from row 512 and calculated the ensuing wavenumber at the center of the detector.

With these data, I searched for minimum residuals between the observed and calculated wavenumber:

wn_calc = order * 1d4 / ( d * sin (alpha) + sin(beta) )

d = the groove spacing and was allowed to vary by +-5%

alpha = the input angle and comes from the measured voltage, the voltage0, and the degrees per volt

          = (V - V0) * deg/volt

V0 was allowed to vary by 2% in my final iteration.

beta = the output angle 

       = alpha + delta  

where delta is the angle between the input and output.  This was allowed to vary by 20% in the final iteration.

I ran a nested loop calculating the residuals over the allowed ranges of d, delta, and V0.  I did this multiple times with different inputs to see if there were local minima.  In fact, delta and V0 play off of each other and provide many different local minima.  The absolute minimum had:

d = 32.5956 microns between grooves

delta = 2.715  degrees between alpha and beta (beta = alpha + 2.715)

v0 = 3.2363 volts for when the echelle is at 0 degrees

By the way, the values given got all residuals < 0.2 cm-1 with the median abs(residual) = .024 cm-1

High-medium slit resolutions for 7.5um

This setting uses close to the same angle as for the 4th order Q-branch of C2H2 with filter=14um.
We use the filter=7.466um to acquire H2O lines in 7th order near 1315cm-1. The spectra were taken with the gas cell rinsed and continually pumping.

The line FWHM had a scatter of between 0.5 and 0.84 in stddev for the eight lines reported here, compared to about 0.4-0.5 for the 6 lines in the 13.7um. I'm not sure what that means, except maybe we should look for a C2H2 set of lines next time for doing resolution tests. 

Using R=816800/FWHM found from 13.7um tests to calculate resolution.

This data is in B_12_02_28/
filename    slit             1           3           5           6           7           8         11        12    med(FWHM)    R
b003    3.5km/s    10.41    10.28    11.27    11.53    10.88    10.99    11.19    10.30    10.99    74307
b004    2.7km/s      8.96     9.17      9.85     10.23     9.64      9.69    10.17      9.00       9.69    84259
b005    2.0km/s      8.23     8.48      9.09      9.64      8.91      8.99     9.80       8.33       8.99    90858
b006    1.5km/s      7.75     7.83      7.77      8.89      8.39      8.60     9.15       7.66       8.39    97406
b008    6.0km/s    14.77    14.00    15.79    16.24    14.59    15.13    14.36    13.88    14.77    55304
b009    4.5km/s    12.05    11.75    13.11    13.49    12.13    12.44    12.38    11.52    12.38    65972

High-medium slit resolutions for 18um

Same echelle voltage/angle as 4th order Q-branch of C2H2 except with filter=18a instead of 14um. There are 3 H2O lines in 3rd order near 520cm^-1. All images were taken with the gas cell rinsed and continually pumping.

Same measurement procedure as for high-medium slit resolutions at 14um. As there are only 3 lines available, I list the median of the  FWHM from Gaussian fits to the 20 innermost columns of each line.

Line 1: 547.82
Line 2: 546.30
Line 3: 545.30


All files are from B_12_02_24/
#filename slitfeature line1_FWHM line2_FWHM   line3_FWHM
b022.fits    17km/s     -        32.08        33.61
b023.fits    6.0km/s    13.77    12.25        13.45
b024.fits    4.5km/s    11.57    10.18        11.34
b025.fits    3.5km/s    10.32     8.89        10.15
b026.fits    3.5km/s    10.36     8.87        10.16
b027.fits    2.7km/s     9.52     7.94        8.98
b028.fits    2.0km/s     9.15     7.56        8.54
b029.fits    1.5km/s     8.82     7.34        8.26

High-medium, 14um slit resolutions

Experiment: Mapping the slit wheel features for the best case spectral resolution (where the echelle mirror was at 17 turns and the echelon mirror was at 16.5 turns)

These images are located in B_12_02_24/

Procedure:
1. subtracted 4th frame from the 1st frame of each SUTR image.

2. Selected the Q-branch lines 10-15

3. Fit 6 parameter Gaussian functions across the y-axis for +/- 10 pixels in x dimension-- then took thed median of this measurement.

4. To correct for the broadening due to the slope of the line, I fit the slope of each line, and found the correction factor: cos(arctan(slope))-- > true sigma= raw sigma x cos(arctan(slope)). Typical angles from East are about -23 degrees.

5. Multiplied the sigma values by 2*sqrt(2*ln(2)) to obtain FWHM values.

6. Found pixel scale (um/pix) by fitting a line to the wavelengths and median y-values of Q-branch lines. (for Q-branch: [10,11,12,13,14,15], I adopted these wavenumbers:
wavenums=[729.65,729.75,729.86,729.97,730.10,730.23].)

7. Below I report the filename, slit wheel feature, median FWHM (pix), minimum FWHM (pix), median resolution, maximum resolution.

(Clarifying: The median FWHM is the median value of the FWHMs obtained for 6 lines. The minimum FWHM is the minimum value within that set of 6 line FWHM. The FWHM value for each line is itself a median value of the width obtained for 20 crosscuts of the line in question. The min(FWHM) for the 17km/s slit is a glitch-- however, I supervised the fits of the other slits 1.5-6.0km/s and the minimum values of the FWHM seem to be reliable).

#filename
#filename    feature    med(FWHM) min(FWHM) med(R)  max(R)
b013.fits    1.5km/s    8.04      7.52    103497.   108617.
b014.fits    2.0km/s    8.57      8.08    95558.    101104.
b015.fits    2.7km/s    9.35      8.81    89326.    92788.
b016.fits    3.5km/s    10.75    10.17    78146.    80317.
b017.fits    4.5km/s    12.25    11.99    66808.    68154.
b018.fits    6.0km/s    14.56    14.02    56419.    58271.
b019.fits    17.km/s    37.29    24.51    23178.    33320.

Acceptance Angle of EXES

On 2/29/2012 we (MJR, JMB and CD) measured the input cone of EXES. We used the tip of a 700F soldering iron as a probe, and moved the iron along a piece of graph paper located 25.75" in front of the window (22" from front of the flange to the graph paper; the flange ring is 4.125" inches in width, and the back surface of the lens penetrates 0.375" into the flange ring: 22 +/- 0.25 + 4.125 - 0.375 = 25.75")

We used the 4.7um filter and the 1.5 km/s slit, and acquired continuously, watching the flux graph as the soldering iron top was moved along the graph paper.

[The proper orientation to scan along the slit was established by procedure X.]

We watched the flux graph and marked the position of the soldering iron tip when the flux was at half maximum.
The total width between half-maxima was 6.2 graph squares or (0.25"/graph square)*6.2=1.55"

Therefore, the half-angle of acceptance is:
arctan(1.55/2/25.75)= 1.724 deg= 0.30088 rad

==> 0.002844 Steradians

Error guess forthcoming...

Followup high-medium focus tests

We pushed a little further on the echelle mirror screw to see if we could get addition improvement in the best focus over the values attained at echelle +15 (see blogpost "Pinhole focus tests")

These are once again pinhole spectra taken in hires mode of the Q-branch of acetylene. Here we report the median and stddev of 5 line width measurements fit with clickfit.pro.

All files are in /B_12_02_24/


#filename echelle_mirror_position echelon_mirror_position spatial_FWHM sig_spatial_FWHM spectral_FWHM sig_spectral_FWHM

b002.fits    15    22.5    9.91    0.65    7.01    0.58
b003.fits    15    20.5    8.41    0.45    6.87    0.51
b004.fits    15    18.5    7.66    0.38    6.92    0.34
b005.fits    15    16.5    7.45    0.36    7.64    0.28
b006.fits    15    14.5    7.65    0.43    8.85    0.51
b007.fits    17    12.5    7.37    0.43    8.63    0.50
b008.fits    17    14.5    7.04    0.29    7.30    0.51
b009.fits    17    16.5    7.19    0.28    6.48    0.60
b010.fits    17    18.5    7.77    0.32    6.67    0.60
b011.fits    17    20.5    8.99    0.49    6.72    0.60
b012.fits    17    16.5    7.25    0.35    6.66    0.56

The best spectral focus is at 17 turns on the echelle mirror screws and 16.5 turns on the echelon mirror screws.

Medium Res Pinhole data

We took 14um Q-branch data while in medium res mode to evaluate the spatial and spectral focus while the echelle mirror was placed at different settings in the range of +8 turns to +15 turns. We used clickfit for all measurements. The images were 4SUTR, so we first made a single frame by subtracting frame4 from frame1 for each image. Then we rotated the images in IDL with the rotate(im,1) function. 

Then clickfit,/box was used on the region from point (200,500)--> (700,700), encompassing
most of the Q branch and some of the R-branch. We selected a sequence of 5 odd-numbered Q-branch lines to fit (something like 7-9-11-13-15, but I will determine this and update the post soon) and used these lines to fit 1-D Gaussians to. The tabular data below shows the median FWHM of the line fits and the standard deviation.
The plots show all measurements of the median FWHM values.

Once I identify the lines we used, I'll be able to get the pixel/wavelength scale and report the spectral resolutions. 

These files are in B_12_02_03/
#filename     echelle_mirror_position spatial_FWHM stddev(spatial_FWHM)  spectral_FWHM stddev(spectral_FWHM)
636    12    5.55    0.50    5.10    0.39
637     8    6.12    0.55    5.54    0.50
638    10    5.51    0.49    5.23    0.48
639     9    5.73    0.51    5.40    0.65
640    11    5.45    0.48    5.19    0.48
641    12    5.54    0.54    5.10    0.45
642    13    5.81    0.57    5.17    0.47
643    14    6.36    0.63    5.16    0.49
644    15    7.38    0.73    5.31    0.48
645     9    5.74    0.51    5.36    0.99
646    10    5.50    0.49    5.38    0.51
647    10    5.51    0.49    5.39    0.67
648    11    5.46    0.53    5.20    0.45
649    12    5.54    0.50    5.12    0.47
650    13    5.81    0.58    5.13    0.38
651    11    5.47    0.48    5.26    0.25

It appears that +12 had the best spectral focus, and +11 was the best spatial focus. 

6.2 micron filter curve

The 6.2 micron filter arrived from Univ of Reading's IR Multilayer Lab today.  There are 5 filter+MgF2 blocker combinations.  The figure below is extracted from the documentation and is the cold transmission curve.  Full documentation, including XLS spreadsheet of transmission, is on NSCKN.