SpectroPhotCal

Calibration of Spectrophotometric Standards from the Ground

Jonathan Burkle, Nick Mostek, Stuart Mufson

Indiana University

During this summer, REU student Jon Burkle (Wheaton College), working in collaboration with Stuart Mufson and Nick Mostek, investigated whether SNAP fundamental spectrophotometric standards could be calibrated from the ground, relative to a light source, in narrow spectral bandpasses free of water vapor and other sources of opacity. As a reminder, the SNAP fundamental spectrophotometric calibrators, at least in the current calibration plan, have not been measured relative to a calibrated light source in the near infrared, but are assumed to be calibrated sufficiently accurately by stellar atmospheres models. Our long range goal is to test whether these stellar atmospheres models are consistent with the stellar fluxes in select narrow band filters calibrated relative to a light source. If they are consistent, then the SNAP collaboration can have confidence in the calibration of the supernova data, which ultimately derives from the calibration of the fundamental standards. If the fluxes are not consistent, then the SNAP collaboration will need to invest more heavily in the near infrared calibration of the fundamental photometric standards. The reason for the R&D described here is to test whether such an experiment is even feasible.

We investigated the three bandpasses shown below. These bandpasses all had commercially available interference filters that were purchased from Oriel.

1050 nm, 10 nm bandpass: As seen below, this bandpass is virtually free of opacity
1200 nm, 10 nm bandpass: This filter has approximately 1% attenuation in its bandpass
1400 nm, 80 nm bandpass: This filter is heavily obscured by water vapor

The R&D effort this summer had two components.

I. 1/R**2 Tests

We first measured a calibrated light source under constant temperature and humidity conditions in the lab at both 7.8m and 8.5m ('near') to test the accuracy at which we could measure 1/R**2. Our measuring apparatus in the near infrared consisted of a single channel photometer equipped with a Hamamatsu 3mm, thermoelectrically cooled InGaAs detector. For the R-band measurements, a Hamamatsu Si-photodiode replaced the InGaAs detector. The photometer was mounted on an F10 Meade 8-inch reflecting telescope. The DAQ used Vernier LoggerPro hardware and software. The relative humidity was constantly monitored with a Vernier humidity meter that was read out simultaneously. The light source was a calibrated 45W QTH Oriel light source powered by a regulated power supply. Laboratory measurements by Nick Mostek using a calibrated Si photodiode and a calibrated InGaAs detector were used to verify the lamp calibration. (See Nick's talks at the hardware meetings for more information.)

In Fig.1 we show a scatter diagram of the laboratory 1050 nm bandpass measurements (first 41 trials). What is shown is the fractional error in the measurements (not % error):

[measured(flux at 8.5m/flux at 7.8m)**2 - expected (flux at 8.5m/flux at 7.8m)**2]/expected(flux at 8.5m/flux at 7.8m)**2

Figure 1. Scatter diagram of the fractional error in the 1/R**2 'near' measurements at 150 nm

A histogram of the laboratory measurements (first 41 trials of the scatter diagram) is shown in Fig.2(a). (the unreadable abscissa is now % error) The distribution is reasonably Gaussian. We repeated the measurements at 7.8m and 8.5m on the Swain Hall roof in conditions of > 95% relative humidity. These measurements are shown in Fig.1 for trials 42 and above. Although the measurements are systematically lower than the lab measurements (i.e., less light than expected), the systematics in the measurements most likely make the difference insignificant. The Swain Hall roof is made up of tiles that move whenever people walk over them which can cause the flux ratios to vary by 1-2% as the observer moves the light source back and forth. In addition, the distribution of the measurements do not differ significantly from a Gaussian.

Figure 2. (a) Laboratory 'near' measurements of 1/R**2 in the lab at 1050 nm. (b) All 'near' measurements of 1/R**2 at 1050 nm (lab + roof)

In Table 1 we summarize the results of the 'near' measurements in the lab through the 1050nm filter. In Table 2 we give the absolute flux normalization at 7.8m in the 1050nm filter.

In Fig.3(a) we show the histogram of the measurements at 1400 nm in the lab and in Fig.3(b) the measurements in the lab and on the roof of Swain Hall. In this case the effect of water vapor on the ratios is clearly apparent and statistically significant. These results are summarized in Table 1. In Table 2, we give the absolute flux normalization at 7.8m in the 1400nm filter.

Figure 3. (a) Laboratory 'near' measurements of 1/R**2 in the lab at 1400 nm. (b) All 'near' measurements of 1/R**2 at 1400 nm (lab + roof)

The measurements at 1200nm, as well as measurements at R-band, in the lab are also summarized in Table 1. The absolute flux normalization at 7.8m is given in Table 2.

We then made measurements of the calibrated light source through the same filter set from the roof of Swain Hall and the roof of the Indiana University Law Library, which was surveyed by the Indiana Geological survey to be 124.1m distant. In principle, the flux from the lamp should illuminate the telescope like the light from the star. At 124.1m, the 4mm lamp filament has a angular size of 6.6". Although the signal strength was sufficient to move the source farther back, thre was no way to do this without falling off the roof. We do not believe this to have a significant effect in our measurements. These measurements were made over a period of 6 weeks and were quite repeatable.

The results of the 1/R**2 mesurements between the Swain Hall roof and the Law Library roof are given in Table 1. In all bandpasses there is a clear and significant deficit relative to the expected 1/R**2 law over a 124.1m baseline. At 1050nm in particular, there is no obvious reason for this discrepancy. But the deficit clearly grows as the atmospheric opacity grows, as it should. The sightline is bordered on the north by woods and on the south by a well-travelled street. It passes directly over a fraternity house, although the house is currently vacant during the summer recess.

Table 1
The flux ratio, F/F0, measured in the lab at 7.8m and 8.5m, and on the Law Library roof at 124.1m through filters centered at 1050nm, 1200nm, 1400nm, and R-band normalized to the fiducial flux at 7.8m. The table gives for each filter at 8.5m and 124.1m the measured ratio (meas), the expected ratio (exp), and the fractional deviation (D)

F/Fo
	7.8m	8.5m			124.1m
Filter	fid	meas.	exp.	D	meas.	exp.	D
1050nm	1	0.825 + 0.009	0.842	-0.020	0.003266 + 0.00006	0.00398	-0.179
1200nm	1	0.834 + 0.016	″	-0.009	0.003181 + 0.00015	″	-0.201
1400nm	1	0.823 + 0.029	″	-0.023	0.001460 + 0.00005	″	-0.633
R-Band	1	0.826 + 0.010	″	-0.019	0.002346	″	-0.411

Table 2. The absolute flux measured at 7.8m in the filter bandpasses

Filter	F (mW/m²/nm) @ 7.8m
1050	0.03675
1200	0.03339
1400	0.02716
R-Band	0.01808

Fig.4(a) and 4(b) below show the experimental results described above in graphical form. At the 'near' pathlengths, the results conform to the 1/R**2 law. But at the 124.1m pathlength there is a significant deviation from the 1/R**2 law, even at 1050nm where there is no water vapor opacity in the bandpass.

Figure 4. (a) Graphical display of the results in Table 1. The solid line reprents the 1/R**2 law, normalized to 1 at 7.8m. The 'near' mesurements for all filters fall on the line. The 'far' mesurements to the roof of the Law Library for all filters clearly fall below the line.

Figure 4. (b) Enlarged view of the deviation of the 'far' measurements from the 1/R**2 law. Statistical errors in the measurements are small compared with the size of the symbol. The deviations are statistically significant and the deviations increase as the atmospheric absorption increases.

Conclusion: If this approach to the calibration of fundamental SNAP photometric standards is to succeed, this experiment must be repeated at better sites, and over a larger range of pathlengths, to prove whether the 1/R**2 law holds. If environmental effects are responsible for our observed 1/R**2 deficit at 1050 nm, futher measurements at better sites should validate this piece of the calibration procedure.

I. Tests using the Moon

In addition to the 1/R**2 tests described above, we have been testing whether observations of stars would be free of opacity in the narrow bandpass filters in the near infrared. One problem we faced was the fact that our photometer was not an integrating device. Basically we just read a voltage. So we are unable to measure stars, even a star as bright as Arcturus in the near infrared. For a few $100 we could have made an integrator, but we chose a different and cheaper route. We looked at the Moon as a function of zenith angle. This should tell us whether our bandpasses are clear. So far our results are problematical. But these results were obtained over only a 3 day period and our observations are continuing. We have had uncooperative weather over the past 3 days running. (Indiana, go figure)

In Figs.5-7, we show the results of measurements of the Moon through filters at 1050nm, 1200nm, and 1400nm as a function of zenith angle. The procedure is to align the Meade on a particular feature on the Moon and allow the telescope to track (it has a Moon tracking program). We measured the Moon through each filter twice for 1 minute with 50 ms samples, and averaged the result. We then cycled to the next filter. The instantaneous zenith angle was determined from Voyager III. The Meade's ability to track the Moon is compromised somewhat, however, because the torque on the gears from the photometer is clearly much greater than the motors have been designed for, even though we wrapped the front end of the telescope tube with lead sheet. The gears now obviously have backlash that they didn't have when we began these measurements.

Except for transit on August 9, the results are consistent. The 1050nm bandpass appears clear, the 1200nm bandpass shows the effects of some opacity, and the 1400nm bandpass is affected most by opacity. What happened to double the signal on August 9 near transit? We do not understand this now and only more measurements will enable us to decide whether the effect is real or a systematic introduced by our less than robust setup.

Figure 5. Measurements of the Moon over 3 days in the 1050nm filter as a function of sec(zentih angle)

Figure 6. Measurements of the Moon over 3 days in the 1200nm filter as a function of the sec(zenith angle)

Figure 7. Measurements of the Moon over 3 days in the 1400nm filter as a function of the sec(zenith angle)