Super-SDSS filter - useful notes and the T50% cut points ======================================================== Vik Dhillon @Sheffield 1 March 2017 ----------------------------------- In this directory are contained all of the scripts, data files and plots required to calculate the cut points of the Super-SDSS filters we have ordered from Asahi. There are also some useful scripts to plot the profiles with/without the dichroics. This file contains various useful notes on the Super-SDSS filters, and describes the T50% calculation and results. Asahi require the following information for each filter: The cut-on/off (T50%) wavelength that maximises the throughput when used with the as-built HiPERCAM dichroics. Note that T50% means the *absolute* transmission at 50%, not half of the peak transmission. The theoretical filter profiles I have been sent by Asahi for the Super-SDSS filters are calculated for a parallel incident beam. So, in my scripts, I correct the bandpasses for the actual f/2.47 beam in HiPERCAM, and use these corrected profiles to calculate the optimum T50% wavelengths. Asahi will then take these optimum T50% wavelengths, correct them back to the values for a parallel beam, and make the filters. They will then measure the transmission of the as-built filters in a parallel beam at 0 degrees angle of incidence (AOI), as they always do. Note that the filters will have the same optical thickness as the "normal" HiPERCAM SDSS filters that we have already ordered (and which I used to optimise the dichroic cut points). To do this, Asahi are going to make the Super-SDSS filter substrates the same physical thickness as the clear filters originally made for ULTRACAM. This is because both the clear filters and the Super-SDSS filters are fused silica (the normal SDSS filters use coloured glasses) and the clear filters have the same optical thickness as the other ULTRACAM (and HiPERCAM and ULTRASPEC) filters. Toshihiko confirmed this in an email to me on 12/12/2016: ------------------------------------------------------------- Yes, this is what I understand. We should polish all fused silica substrates with 5.43 mm and our smallest tolerance, better than +/-0.05 mm. My message to you sent on 23 April, 2003. We also checked the thickness of each filter again by micrometer caliper. All ones(No_1,2,3) are same, t=5.43mm. (5.4mm +-0.05) ------------------------------------------------------------- The specifications of the Super-SDSS filters are as follows (from Toshihiko's email dated 12/09/2016): [HiPERCAM g' ~ z' filter] Cut-on and off wavelength tolerance: each +/-5 nm T(average) > 95% or over in passband T > 90% in passband (i.e. valley of ripple must not be less than 90%) T (average) < 0.01% 300 nm - 1100 nm T < 0.1% 300 nm - 1100 nm [HiPERCAM u' filter] Cut-on wavelength tolerance: +4 nm, -6 nm Cut-on wavelength tolerance: +/-4 nm T > 85% or over in passband T (average) < 0.01% 300 nm - 1000 nm T < 0.1% 300 nm - 1100 nm The substrates are fused silica. The transmission curves Toshihiko has sent me for the Super-SDSS filters include just the absorption/reflection losses of the multi-layer coatings, but the transmission of fused silica between 300-1000nm is negligible, so it doesn't matter that Asahi hasn't included this. (But this does need to be included for the normal SDSS filters, of course, as they use coloured glasses.) The original u' filter design that Toshihiko sent me on 12/09/2016 was based on that produced for ODI at WIYN Observatory: http://www.asahi-spectra.com/opticalfilters/large_filters.html This has a blue-side cutoff around 330nm. I asked Toshihiko if this can be pushed further to the blue on 15/09/2016. He responded saying that in this case we'd be better off with the u' filter design that Asahi provided for DECam in 2012. According to Toshihiko, the DECam u' filter is a "short pass type u' filter without the long pass film" (i.e. without the coating to define the blue wing). However, even by not adding the long pass coating, the transmission still decreases around 330 nm due to the absorption of coating material (Ta2O5), although not as badly as in the ODI filter. Toshihiko attached the revised transmission spreadsheet (containing the DECam u' filter rather than the ODI one) on 29/09/2016, and this is the one that I use for the T50% calculations. To quantify, check out compare_u_filters.pdf and compare_u_filters.py, which gives the following output for the SDSS u' filter, Super-SDSS DECam u' filter and Super-SDSS ODI u' filter. Transmissions: -------------- OLD u' theoretical transmission = 63.75 % SUPER DECam u' theoretical transmission = 89.68 % SUPER ODI u' theoretical transmission = 69.79 % SUPER DECam u'/OLD u' improvement = 40.67 % SUPER ODI u'/OLD u' improvement = 9.47 % So, I now need to calculate the optimum T50% wavelengths. I modified the scripts I'd written to calculate the optimum dichroic cut points (named dichroics/dichroic_cutpoints_ug.py, etc). These new scripts are called filters/super_sdss/filter_cutpoint_ug.py, and the plots are in the corresponding .pdf files, etc. The new scripts do the following (a bit of a cheat): - They load in the as-built dichroics and the theoretical Super SDSS filter profiles. - It then steps the as-built dichroic transmission curve by +/-15nm about its as-built position, and calculates the instrument throughput at each step in u', g' and in u'+g'. - The number of nm that the as-built dichroic has to step by to give the maximum throughput in Super SDSS u'+g'/2 (i.e. the average throughput in the combined u' and g' bands) is only +1nm, with an approximate error of +/-1nm (the step size). As a check, I stepped the u' filter by +1nm, and got an optimum step on 0nm, as expected. So there is no point at all in shifting the Super SDSS u' and g' filters at all from their theoretical bandpasses sent to me by Toshihiko. - In the filter_cutpoint_ug.pdf plot I show a solid vertical line, which is the wavelength of the absolute 50% dichroic transmission (t50%). I also a vertical dashed line which shows where the t50% line needs to be moved in order to optimise the u'+g' throughput. The corresponding values are also listed on the plot as lambda_50 and lambda_c, respectively. - Note that in the above script, I shift the Super-SDSS bandpasses to account for their use in an f/2.47 beam. I get the following values for the u'g'r'i'z' filters in nm, respectively: 1.56263737133, 2.11968662262, 2.75054050657, 3.37041155829, 3.99643299606 Toshihiko got the following values in his email of 10/02/2016: ------------------------------------------------------------- If it is still difficult to have time, may I "propose" the cut-on/off wavelengths you would probably accept? We need to know *just* the information about your favorite wavelengths about r, i, and z-band first in HiPERCAM (i.e. f/2.47 beam) in consideration of actual HiPERCAM dichroics response. We already calculated the wavelength difference between an f/2.47 beam and parallel beam at AOI 0 deg. (We will measure the transmission of filters in a parallel beam at normal incidence.) We must consider these numbers when we coat. Calculated wavelength shift In a parallel beam at AOI 0 deg => In an f/2.47 beam [Super SDSS r-band] Cut-on: 1.7 nm blueward Cut-off: 2.18 nm blueward [Super SDSS i-band] Cut-on: 2.3 nm blueward Cut-off: 2.67 nm blueward [Super SDSS z-band] Cut-on: 2.77 nm blueward ------------------------------------------------------------- My values seem to be about 1nm larger than Toshihiko's, no doubt because he uses an accurate value for the refractive index of the glass (I just use 1.5). If I use n=1.7, I get the following shifts: 1.21539445594 1.64865849028 2.13932659225 2.62145242226 3.10836192457 These are in much better agreement with Toshihiko's, so I've adopted these. Note that I have just one value for the whole filter, not one for each side of the filter. The maximum error introduced by doing this is about 0.3nm, so not worth bothering about. I reran the filter_cutpoint_ug.py script with the revised refractive index, and got more or less the same answer, so all good. I also wrote a script called filters/super_sdss/filter_t50.py This calculates the wavelength at which the transmission has an absolute value of 50% in the blue and red wings of each filter. The values are calculated using the theoretical Super SDSS filter profiles sent to me by Toshihiko, at an AOI=0 degrees, i.e. the f/2.47 bandpass shift is not taken into account. These are the values I'll give to Toshihiko, assuming all of the filters are like u' and g' and show no evidence that the bandpasses need to be shifted prior to manufacture. I get the following values from this script, which are what I shall give Toshihiko: u' blue-wing 50% transmission wavelength = 311.125171248 u' red-wing 50% transmission wavelength = 390.11548414 Make blue wing of u' as blue as possible, although the current cut is fine. Red wing of u' needs a +1nm shift. Blue wing of g' requires NO shift. g' blue-wing 50% transmission wavelength = 400.344008378 g' red-wing 50% transmission wavelength = 550.112919999 Red wing of g' needs a -1nm shift. Blue wing of r' requires NO shift. r' blue-wing 50% transmission wavelength = 550.077075804 r' red-wing 50% transmission wavelength = 685.899881984 Red wing of r' and blue wing of i' require NO shifts. i' blue-wing 50% transmission wavelength = 695.006022417 i' red-wing 50% transmission wavelength = 835.923304342 Red wing of i' needs a +5nm shift. Blue wing of z' required NO shift. z' blue-wing 50% transmission wavelength = 833.288971168 I estimate that the error in my calculation is +/-1nm, so you can see that there is no change required to the u'g'r' and z' filters. The red wing of the i' filter would be best with a +5nm shift, but this is only ~0.5% of the wavelength of the red wing, so I imagine this is probably within Asahi's manufacturing error? If so, my conclusion would be that the Super-SDSS filter profiles require NO CHANGES compared to the theoretical profiles that Toshihiko sent me on 29/09/2016.