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MASTER Absolute Photometric Calibration for observations with polarizers and B V RI filters v0.3. December 2013
1. Zero points for obsevations in polarizers. Average effective wavelengths and band widths for various sp ectra
Lyrae spectrum f flat k å 1014 Hz 5386 ± 18 4.66 ± 0.04 5714 ± 12 4.1 6234.5 ± 0.5 1.03 5372 ± 18 4.69 ± 0.04
eff 2

Optical Filter ID 1 2 3 4

a

Fo c -6 10 erg/cm2 s 12.55 ± 0.10 11.04 ± 0.01 2.77 ± 0.004 12.63 ± 0.10

fo d 6 10 photons/cm2 s 3.40 ± 0.02 3.18 ± 0.004 0.87 ± 0.002 3.42 ± 0.02

Power-law eff f 2 å 5746 ± 317 6197 ± 253 6305 ± 31 5736 ± 316

spectra pl k 1014 Hz 3.70 ± 0.26 3.14 ± 0.16 0.88 ± 0.01 3.70 ± 0.27

Table 1. Calibration parameters for MASTER observations with polarizers. Average values for two atmospheric transmissions (MK+Pa); details are given in Tables 3 and 4. In the case of the power-law spectra, the values have also been averaged between four spectra, with power-law index = 0, 0.5, 1, 1.5 (see Table 4). Plus-minus values just show the span of values for different cases. See description of superscript indexes in the text.

Optical Filter ID B+CCD V+CCD R+CCD I+CCD

Fo c -6 10 erg/cm2 s 6.28 ± 0.01 3.26 ± 0.002 2.66 ± 0.003 1.86 ± 0.001

fo d 6 10 photons/cm2 s 1.38 ± 0.002 0.8715 ± 0.0005 0.83 ± 0.001 0.7555 ± 0.0005

Lyrae spectrum eff f flat k 2 å 1014 Hz 4366 ± 2 1.69 5318 ± 1 0.92 6212 ± 1 0.91 8060.5 ± 0.5 0.80

Power-law spectra eff f pl k 2 å 1014 Hz 4378 ± 23 1.56 ± 0.02 5342 ± 13 0.88 6277 ± 29 0.84 ± 0.01 8143 ± 43 0.76 ± 0.01

Table 2. Calibration parameters for MASTER (MK+Pa); details are given in Tables 5 and 6. four spectra, with power-law index = 0, 0.5, cases. See description of superscript indexes in

observations with B V RI filters. Average values for two atmospheric transmissions In the case of the power-law spectra, the values have also been averaged between 1, 1.5 (see Table 6). Plus-minus values just show the span of values for different the text.

If an investigated spectrum is exactly power-law, expressions (2) and (4) below will give the exact values for the spectral flux density, provided we substitute eff as the effective wavelength and pl as effective frequency range, 2 adopting their values from Table 4. For spectra of any form, but resembling power-law, expressions (2) and (4) are approximate. While the value fobs (see the description of index d below) should correspond accurately to the photon flux from a source with an arbitrary spectrum, the calculated Fobs and tabulated ef f are approximate. 2 When some degree of the linear polarization is actually observed, this should be taken into account (see section 2). a See Fig. 1 for the normalized transmissions of the filters and CCD. 1 2 3 4 CCD CCD â Polarizer 1 -- before January 2011 CCD â R-filter â Polarizer -- January­July 2011 CCD â Polarizer2 -- after July 2011 (new polarizer)

b Three atmospheric extinction wavelength dependences are used: 1) no atmosphere (or "gray" atmosphere) ; 2) Atmospheric extinction properties above Mauna Kea (Buton et al. 2013) for air mass unity. 3) Mean extinction coefficient for Palomar mountain (Hayes & Latham 1975) for air mass unity. The atmospheric transmission is expressed as 10-k() sec z , where k () is the extinction coefficient [mag/air mass], the air mass is sec z , and z is the zenith distance.
high contrast Linear Polarizing Films, http://www.edmundoptics.com/optics/polarizers/linear-polarizers/high-contrast-linearpolarizing-film/3435 2 Ultra Broadband Wire Grid Polarizers, http://www.edmundoptics.com/optics/polarizers/wire-grid-polarizers/ultra-broadbandwire-grid-polarizers/3330 (Kornilov et al. 2012; Ahn et al. 2005) Article number, page 1 of 7page.7
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c To convert observed magnitudes into the absolute units, the zero-point factor Fo is needed: F
obs

= Fo 10-

0.4 m

[erg/cm2 s],

(1)

where m is the observed magnitude and Fo is calculated as follows
max

Fo =

min

S R()d ,

where S is the spectrum of a source with zero magnitude before entering the Earth's atmosphere [erg/cm2 s å]. We take S as the Vega spectrum from Bohlin (2007). The band transmission R() is the product of the filter, CCD, and atmospheric transmissions, normalized by its maximum value. Then, we can estimate the spectral flux density at some effective wavelength eff in the following way: F F
obs

/ [erg/cm2 s Hz],

(2)

where the effective frequency range is given in paragraph k. d To calculate the integrated absolute flux in a wide band, it is more robust to use units of photons/cm2 s, as CCDs are the photon-counting detectors. The computation is similar to the previous case: fobs = fo 10-

max

0. 4 m

[photons/cm2 s],

(3)

fo =

min

N R()d ,

where min and max are boundary wavelengths where R() is nonzero, N is the spectral photon-number-flux density of a source of zero magnitude before entering the Earth's atmosphere. N can be derived from S as follows N = S


. hc
eff

To find the spectral flux density, two more values are needed, F h

and , (4)

c fobs / [erg/cm2 s Hz]; eff

Note that

f fobs / [photons/cm2 s Hz].

e­j The effective wavelengths may be defined in several ways. Some of them depend on the spectrum of the source.
max max
max

R() d
eff 1

S R() d ;
eff 2

N R() d ;
eff 3

=

min max

=

min max

=



min

max

; N R ( ) d

R ( ) d

min

S R ( ) d

min

min



max

max

c = eff 4

R(c/ ) d

min



max

; R(c/ ) d

c = eff 5

S R(c/ ) d
min max

. S R(c/ ) d

min



min

In the last expression we use that S = S 2 /c. Expressions (2) and (4) give identical results if one uses eff , as follows 2 from its definition.
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k The effective frequency range depends on the source spectrum. We define
max

S R(c/ )d = If eff = c/eff , the above is identical to 2 = For the power-law spectra S
- min

S (eff )

max

.

N R(c/ )d
min

N (eff )

.

, one has

max

pl =

min

( /eff )- R(c/ ) d

and for the flat spectra

max

S R(c/ )d flat = (max -
min

)



min



max

. S d

min

l Vega spectrum is from Bohlin (2007).

2. Non-zero degree of linear polarization
If the magnitude m is observed with the polarizer oriented at 0o , and the full information about the linear polarization is gained, the form of (1) should be modified as follows: Fobs = Fo 10-0.4 m [erg/cm2 s], 1 - PL + 2PL cos2

where Fobs is the full energy flux (integrated over all polarization angles), the value Fo is unchanged, PL is the degree of linear polarization, is the polarization angle. Expression (3) should be modified in the same way. The above ralation is a consequence of the fact that the flux observed through a polarazer at 0o can be written as F (0o ) = Fobs (1 - PL ) + PL Fobs cos2 . 2

3. Zero points for observations in B V RI filters. Average effective wavelengths and band widths for various spectra
MASTER B , V , R and I filters represent the Johnson-Cousins system. Averaged values for two atmospheric conditions are presented in Table 2. Details are given in Tables 5, 6 and Fig. 2.

If you have any questions, please contact Galina Lipunova (galja@sai.msu.ru) or Maria Pruzhinskaya (pruzhinskaya@gmail.com).

References
Ahn, S.-W., Lee, K.-D., Kim, J.-S., et al. 2005, Nanotechnology, 16, 1874 Bohlin, R. C. 2007, in Astronomical Society of the Pacific Conference Series, Vol. 364, The Future of Photometric, Spectrophotometric and Polarimetric Standardization, ed. C. Sterken, 315 Buton, C., Copin, Y., Aldering, G., et al. 2013, A&A, 549, A8 Hayes, D. S. & Latham, D. W. 1975, ApJ, 197, 593 Kornilov, V. G., Lipunov, V. M., Gorbovskoy, E. S., et al. 2012, Exp erimental Astronomy, 33, 173

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Optical Filter ID 1 2 3 4 1 2 3 4 1 2 3 4

Atmosph.b
a

10 No No No No Pa Pa Pa Pa MK MK MK MK

-6

Fo c erg/cm2 s

13.206 11.068 2.724 13.299 12.446 11.031 2.772 12.529 12.648 11.049 2.763 12.735

fo d eff e 1 2 10 photons/cm s å Spectrum: Lyrae l 3.501 6095 3.142 6527 0.853 6345 3.517 6088 3.386 6265 3.180 6620 0.870 6358 3.399 6257 3.418 6224 3.172 6597 0.867 6357 3.432 6216
6



eff 2

f



eff 3

g



eff 4

h



eff 5

j

å 5267 5639 6224 5253 5404 5726 6235 5389 5369 5702 6234 5354

å 5574 5916 6261 5559 5710 6009 6272 5694 5675 5984 6271 5659

å 4918 5597 6228 4919 5131 5687 6239 5124 5080 5663 6238 5074

å 4998 5399 6190 4989 5135 5480 6200 5122 5100 5457 6199 5087

flat k 1014 Hz 4.90 4.11 1.01 4.94 4.62 4.10 1.03 4.65 4.70 4.10 1.03 4.73

Table 3. Zero-point factors, effective wavelengths, and rough effective frequency range for the Lyrae spectrum. See the description of the superscript indexes in the text.

Fig. 1. Passbands normalized transmission.

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Optical Filter ID 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

Atmosph.b
a



eff 1

e



eff 2

f



eff 3

g



eff 4

h



eff 5

j

å No No No No MK MK MK MK Pa Pa Pa Pa No No No No MK MK MK MK Pa Pa Pa Pa No No No No MK MK MK MK Pa Pa Pa Pa No No No No MK MK MK MK Pa Pa Pa Pa 6095 6527 6345 6088 6224 6597 6357 6216 6265 6620 6358 6257 6095 6527 6345 6088 6224 6597 6357 6216 6265 6620 6358 6257 6095 6527 6345 6088 6224 6597 6357 6216 6265 6620 6358 6257 6095 6527 6345 6088 6224 6597 6357 6216 6265 6620 6358 6257

å å å Spectrum: S 0 5273 5672 4918 5876 6190 5597 6265 6304 6228 5269 5664 4919 5431 5818 5080 5947 6262 5663 6275 6314 6238 5421 5807 5074 5481 5864 5131 5972 6286 5687 6276 6316 6239 5471 5853 5124 - 1 /2 Spectrum: S 5468 5881 4918 6029 6356 5597 6284 6324 6228 5462 5874 4919 5621 6020 5080 6101 6428 5663 6294 6335 6238 5610 6010 5074 5669 6064 5131 6126 6452 5687 6296 6337 6239 5658 6054 5124 -1 Spectrum: S 5672 6095 4918 6190 6527 5597 6304 6345 6228 5664 6088 4919 5818 6224 5080 6262 6597 5663 6314 6357 6238 5807 6216 5074 5864 6265 5131 6286 6620 5687 6316 6358 6239 5853 6257 5124 Spectrum: S -1.5 5881 6309 4918 6356 6699 5597 6324 6367 6228 5874 6304 4919 6020 6428 5080 6428 6768 5663 6335 6379 6238 6010 6423 5074 6064 6465 5131 6452 6790 5687 6337 6381 6239 6054 6460 5124

å 4918 5597 6228 4919 5080 5663 6238 5074 5131 5687 6239 5124 5089 5732 6246 5088 5250 5800 6256 5242 5301 5825 6257 5292 5273 5876 6265 5269 5431 5947 6275 5421 5481 5972 6276 5471 5468 6029 6284 5462 5621 6101 6294 5610 5669 6126 6296 5658

flat k 1014 Hz 4.19 3.25 0.86 4.19 3.94 3.27 0.88 3.95 3.86 3.28 0.88 3.87 4.19 3.44 0.95 4.19 4.00 3.49 0.97 4.01 3.94 3.50 0.97 3.95 4.13 3.57 1.01 4.12 3.99 3.63 1.03 4.00 3.95 3.66 1.03 3.95 3.99 3.61 1.04 3.99 3.92 3.71 1.06 3.91 3.89 3.73 1.06 3.89

pl m 1014 Hz 4.19 3.25 0.86 4.19 3.94 3.27 0.88 3.95 3.86 3.28 0.88 3.87 4.08 3.19 0.86 4.08 3.84 3.21 0.88 3.85 3.77 3.22 0.88 3.77 3.90 3.09 0.86 3.90 3.68 3.11 0.87 3.69 3.61 3.12 0.87 3.62 3.66 2.95 0.85 3.66 3.47 2.97 0.87 3.47 3.41 2.98 0.87 3.41

Table 4. Effective wavelengths, "flat" and "power-law" effective frequency range computed using the different power-law spectra. See the description of the superscript indexes in the text.

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Optical Filter ID B+CCD V+CCD R+CCD I+CCD B+CCD V+CCD R+CCD I+CCD B+CCD V+CCD R+CCD I+CCD

Atmosph.b

10 No No No No MK MK MK MK Pa Pa Pa Pa

-6

Fo c erg/cm2 s 6.384 3.255 2.616 1.857 6.293 3.255 2.657 1.862 6.272 3.259 2.663 1.864

fo d eff e 1 2 10 photons/cm s å Spectrum: Lyrae l 1.397 4392 0.870 5359 0.816 6313 0.752 8210 1.382 4408 0.871 5361 0.830 6324 0.755 8214 1.378 4414 0.872 5363 0.832 6325 0.756 8216
6



eff 2

f



eff 3

g



eff 4

h



eff 5

j

å 4348 5315 6202 8056 4364 5317 6211 8060 4369 5319 6213 8061

å 4373 5331 6236 8110 4388 5333 6245 8114 4393 5335 6247 8116

å 4313 5312 6206 8045 4330 5313 6215 8048 4335 5315 6216 8050

å 4325 5300 6171 8006 4340 5302 6180 8009 4345 5304 6181 8010

flat k 1014 Hz 1.72 0.92 0.90 0.79 1.69 0.92 0.91 0.80 1.69 0.92 0.91 0.80

Table 5. Zero-point factors, effective wavelengths, and rough effective frequency range for the Lyrae spectrum. See the description of the superscript indexes in the text.

1

Normalized transmission

0.8

B V R I CCD

0.6

0.4

0.2

0

3000

4000

5000

6000

7000 8000 9000 10000 11000 12000 Wavelength (A)

Fig. 2. Passbands and CCD normalized transmission.

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Optical Filter ID B+CCD V+CCD R+CCD I+CCD B+CCD V+CCD R+CCD I+CCD B+CCD V+CCD R+CCD I+CCD B+CCD V+CCD R+CCD I+CCD B+CCD V+CCD R+CCD I+CCD B+CCD V+CCD R+CCD I+CCD B+CCD V+CCD R+CCD I+CCD B+CCD V+CCD R+CCD I+CCD B+CCD V+CCD R+CCD I+CCD B+CCD V+CCD R+CCD I+CCD B+CCD V+CCD R+CCD I+CCD B+CCD V+CCD R+CCD I+CCD

Atmosph.b



eff 1

e



eff 2

f



eff 3

g



eff 4

h



eff 5

j

å No No No No MK MK MK MK Pa Pa Pa Pa No No No No MK MK MK MK Pa Pa Pa Pa No No No No MK MK MK MK Pa Pa Pa Pa No No No No MK MK MK MK Pa Pa Pa Pa 4392 5359 6313 8210 4408 5361 6324 8214 4414 5363 6325 8216 4392 5359 6313 8210 4408 5361 6324 8214 4414 5363 6325 8216 4392 5359 6313 8210 4408 5361 6324 8214 4414 5363 6325 8216 4392 5359 6313 8210 4408 5361 6324 8214 4414 5363 6325 8216

å å å Spectrum: S 0 4339 4365 4313 5326 5342 5311 6240 6275 6206 8097 8152 8045 4355 4381 4330 5329 5345 5313 6249 6285 6215 8100 8156 8048 4361 4387 4335 5331 5347 5315 6250 6287 6216 8102 8157 8050 - 1 /2 Spectrum: S 4352 4378 4313 5334 5351 5312 6257 6294 6206 8124 8181 8045 4368 4394 4330 5337 5353 5313 6267 6304 6215 8128 8185 8048 4374 4401 4335 5339 5355 5315 6268 6306 6216 8129 8186 8050 -1 Spectrum: S 4365 4392 4313 5342 5359 5311 6275 6313 6206 8152 8210 8045 4381 4408 4330 5345 5361 5313 6285 6324 6215 8156 8214 8048 4387 4414 4335 5347 5363 5315 6287 6325 6216 8157 8216 8050 Spectrum: S -1.5 4378 4405 4313 5351 5367 5311 6294 6333 6206 8181 8240 8045 4394 4422 4330 5353 5370 5313 6304 6344 6215 8185 8244 8048 4401 4428 4335 5355 5372 5315 6306 6346 6216 8186 8246 8050

å 4313 5311 6206 8045 4330 5313 6215 8048 4335 5315 6216 8050 4326 5319 6223 8070 4342 5321 6232 8074 4348 5323 6233 8075 4339 5326 6240 8097 4355 5329 6249 8100 4361 5331 6250 8102 4352 5334 6257 8124 4368 5337 6267 8128 4374 5339 6268 8129

flat k 1014 Hz 1.60 0.88 0.83 0.76 1.58 0.88 0.84 0.76 1.57 0.88 0.84 0.76 1.56 0.87 0.79 0.74 1.54 0.87 0.80 0.74 1.53 0.87 0.81 0.74 1.52 0.85 0.76 0.71 1.50 0.85 0.77 0.71 1.50 0.85 0.77 0.71 1.47 0.83 0.72 0.68 1.46 0.83 0.73 0.68 1.45 0.84 0.74 0.68

pl m 1014 Hz 1.60 0.88 0.83 0.76 1.58 0.88 0.84 0.76 1.57 0.88 0.84 0.76 1.60 0.88 0.82 0.76 1.57 0.88 0.84 0.76 1.56 0.88 0.84 0.76 1.60 0.88 0.82 0.76 1.57 0.88 0.84 0.76 1.56 0.88 0.84 0.76 1.58 0.88 0.82 0.75 1.56 0.88 0.83 0.75 1.55 0.88 0.83 0.76

Table 6. Effective wavelengths, "flat" and "power-law" effective frequency range computed using the different power-law spectra. See the description of the superscript indexes in the text.

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