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The verification of the MASS spectral response
Victor Kornilov Septemb er 14, 2006

Intro duction
The pap er1 shows that the weighting functions (WF) used for turbulence profile restoration from the scintillation indices dep end on the sp ectral distribution of the light incoming on the MASS detector. This sp ectral distribution is defined b oth by the energy distribution in the target star's sp ectrum and by the sp ectral resp onse of the detector, i.e. by the central wavelength 0 and the effective sp ectral bandwidth . The uncertainty of the sp ectral resp onse pro duces errors in the WFs and leads to the systematic errors in the restored turbulence profile. The present pap er studies p ossible sources of uncertainty in the MASS sp ectral resp onse. A recommendation is given on how to reduce the systematic errors of profile restoration in the future and how to correct the data already obtained.

Why the problem exists?
The MASS device includes several optical elements on the path of the incoming light: · · · · the the the the feeding telescop e -- either a Cassegrain system or, more often, a Schmidt-Cassegrain, Fabry lens -- one or two achromatic lenses with visual AR coatings, segmentator -- protected aluminum coating, re-imaging mirrors -- protected aluminum or multilayer dielectric coating.

The transmission of these elements together with the sp ectral sensitivity of the R7400 PMT with bialkali photo-catho de defines the real photometric band of the MASS device. The atmospheric extinction influences the resp onse, to o. The original MASS device had a photometric band that was formed by the PMT sensitivity and the dichroic b eam-splitter (directing red light to the viewer) on the red side and by the cut-off yellow filter like Schott GG420 on the blue side. The transmission features of other optical elements are of little significance. During progressive development of MASS/DIMM devices, several mo difications have b een made to b o ost the efficiency. For example, the few first instruments had re-imaging mirrors coated by multilayer films and included the cut-off filter like GG 455 glass. For these devices, the photometric band was close to the standard photometric V-band but total the transmission was low. At this p oint we had two alternatives -- either to have a well-defined blue cutoff of the MASS sp ectral band and low light signal, or to get a higher signal and some uncertainty in the sp ectral band. The second option was chosen, since there is always a p ossibility to determine or refine the sp ectral resp onse, whereas the noisy data can not b e corrected. Following this decision, the cut-off filters were removed from the devices. The signal increased significantly (for some feeding telescop es). But when the sp ecial element blo cking the blue light was removed, the blue cutoff b ecame strongly dep endent on the UV transmission of other optical comp onents. It seems that these elements do not have any strong depression in the UV transmission
1

Tokovinin A. Polychromatic scintillation. JOSA(A), 2003, V. 20 pp. 686-689

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or reflection co efficients. In this sp ectral domain, the main factor are the AR coatings optimized for the visual. The typical b ehaviors are shown in Fig. 1 for the coatings from Edmund Optics.

Figure 1: Reflectance of a refractive surface with AR coating (on the left). Red curve -- MgF 2 film on BK7 glass, green -- MgF2 on SF5 glass, blue curve -- enhanced multilayer coating for visual light. On the right -- reflectance of Al layer without AR (blue) and with visual AR coating (red). For example, the ESO MASS/DIMM device with the C11 telescop e has 4 reflective and 6 refractive coated surfaces. These surfaces depress greatly the sp ectral resp onse b elow < 400 nm. The absorption in the SF5 glass and in the optical cement in the achromatic lens dominates in the < 350 range. We can not compute exactly the whole MASS and telescop e transmission in the region < 400 nm b ecause many factors are p o orly known. Only crude estimate is p ossible. The direct measurement of the sp ectral transmission of the device is a separate problem that requires a considerable efforts and a sp ecial equipment.

Photometric resp onse curves of various MASS devices

1,0 0,8

PMT B Johnson V Johnson

1,0 0,8

mass mass_dimm without without_cut eso_md elt_mass_dimm

S()

0,6 0,4 0,2 0,0 300

S()
500 600 700

0,6 0,4 0,2 0,0 300

400

, nm

400

, nm

500

600

700

Figure 2: On the left: Photon sp ectral sensitivity of the PMT R7400 from Hamamatsu and the standard photometric bands B and V . On the right: The collection of the MASS sp ectral resp onse curves. The sp ectral resp onses for the different versions of the MASS device are shown in Fig. 2. The curve mass corresp onds to the original MASS that was pro duced in 3 copies. The curve mass dimm is defined for the MASS/DIMM with a yellow cut-off filter and the re-imaging mirrors with multilayer 2


(green) coating. The same devices without filters have the resp onses without and without cut. The latter curve includes the additional UV light losses due to the feeding telescop e and the device optics. The curve eso md characterizes the MASS/DIMM devices with aluminum coated re-imaging mirrors and typical device optics, but without the contribution of the feeding telescop e. It may b e useful when the device is installed on a pure Cassegrain telescop e without visual optimization. On the contrary, with a Schmidt-Cassegrain telescop e optimized for visual observations (like Meade and Celestron telescop es), the elt mass dimm is more adequate. The integral characteristics of the photometric resp onse for the existing versions of the MASS device are listed in the Table 1. Table 1: Integral characteristics of the resp onse curves of the MASS devices. 0 -- central wavelength, ef f -- effective wavelength for A0 V stars, -- effective bandwidth (integral under the curve). All values are shown in nm. Version mass mass dimm without without cut eso md elt mass dimm
0



ef f

103 94 99 88 157 149

Comment Original MASS Yellow filters, green mirrors Green mirrors, TMT telescop e Green mirrors, Meade telescop e Al mirrors, no telescop e Al mirrors, C11 telescop e

475 501 474 486 455 474

469 496 470 479 453 467

Note that we always use the photon sp ectral resp onse, not the energy resp onse. Therefore the energy distributions in the stellar sp ectra must b e in photons, to o.

Quantitative estimation of the effect
First, I studied the changes in the WFs pro duced by the changes in the central wavelength and bandwidth using mo del Gaussian-like resp onse curves. The shift to the blue increases the WFs, the widening depresses the WFs at high altitudes. The over-estimated WFs lead to an under-estimated turbulence intensity while the WF depression at high altitudes results in the apparent increase of the turbulence altitude. For the quantitative analysis of p ossible systematic errors induced by the incorrect choice of the sp ectral resp onse, I use the real curves from Table 1. I designate the set of WFs corresp onding to some photometric resp onse as WF(band). The energy distribution for B0 V star is used b ecause 1) such sp ectrum pro duces the maximum effect and 2) such stars are frequently chosen for measurements. In Fig. 3 (b ottom) the effect pro duced by the shift of 20 nm to the red is illustrated. One can see that the WFs for normal indices are changed by no more than than 5%, the WFs for differential indices are changed by up to 10%. The use of a red-shifted resp onse will overestimate the turbulence integral by 10% and will lead to a small underestimate of the layer's altitude. The upp er part of Fig. 3 shows the ratio of the WF(eso md) to WF(mass dimm). These curves differ significantly in their p ositions and width. Here the differences of the WFs reache 30% for differential and 15% for normal indices. Note that the effect can b e reversed, dep ending on the dominating layer altitude. The complex changes of the WFs for different indices caused by the error in the sp ectral resp onse will likely increase the residuals in the profile restoration. The WFs for without and without cut sp ectral resp onses have maximum difference as large as 25% in the case of AB index. For normal indices, the difference is less than 3%. Similar differences were found in the case of elt mass dimm and mass curves having the same 0 but different . These examples show the upp er limits of p ossible systematic errors pro duced by using a wrong 3


1,3
W1(z)/W2(z)

1,2 1,1 1,0 0,9 0 1,3 5 10 15 20

W1(z)/W2(z)

1,2 1,1 1,0 0,9 0 5

z. km

10

15

20

Figure 3: Upp er plot: the ratio of WF(eso md) to WF(mass dimm). Lower plot: the ratio of WF(eso md) to WF(shifted by 20 nm eso md). The green curves are the normal indices, the violet curves are the differential ones. The dashed curves corresp ond to the A and AB indices.

1,3
W1(z) / W2(z)

1,2 1,1 1,0 0,9 0 1,3 5 10 15 20

W1(z) / W2(z)

1,2 1,1 1,0 0,9 0 5 10 15 20

z, km

Figure 4: Upp er plot: the ratio of WF(without) to WF(without cut). Lower plot: the ratio of WF(elt mass dimm) to WF(mass). These bands differ in and are similar in 0 . sp ectral resp onse. Similar systematic errors arise when a wrong sp ectral class of the target star is used. For example, when the sp ectral typ e G0 I I I is used instead of B0 V, the WFs change in a way similar to the wavelength shift of the sp ectral resp onse.

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The systematic error in the the seeing is ab out half of the WF change, so the error in seeing do es not exceed 15% even in the case when the mass dimm curve is used instead of eso md. In the real situation the error is even less b ecause the whole set of the WFs is used during the restoration, not only WF for AB pair. On the average, the difference in seeing for the case of Fig. 4 (b ottom) is ab out 5% in the relevant altitude domain. For example, the results of turbulence restoration with two different resp onse curves -- the correct one mass and the incorrect one elt mass dimm, are presented in Fig. 5. The night of August 26, 2005 at the Maidanak observatory was chosen due to a high altitude of turbulence on this night. The b oundary layer turbulence app eared o ccasionally. When the incorrect curve is used, the measured seeing increases by 5%. The free-atmosphere seeing (ab ove 1 km) is over-estimated by 2% only. The ro ot-mean-square error of the correct/incorrect seeing ratio is ab out 0.04 and 0.02, resp ectively.

1.4 1.2 1

e, m

0.8 0.6 0.4 0.2 0 17 18 19 20 21 22 23 24

e/m

1.4 1.2 1 0.8 17 18 19 20 21 UT, hs 22 23 24

Figure 5: values E the mass layer, red

Upp er plot: Data of the original MASS device at Maidanak for 2005-08-26. The seeing and M are computed from the profiles restored with the elt mass dimm (circles) and with (line) curves, resp ectively. Lower plot: the ratio E to M (black -- including the 0.5 km -- without this layer).

Verification of the MASS sp ectral resp onse
The MASS device is a highly accurate photometer able to measure the stellar flux to ab out 0 m001 . m002 under go o d sky condition. The base of the simplest verification is a comparison b etween ­0 . the measured star magnitudes in the instrumental photometric system of MASS m M AS S and the catalog magnitudes in the standard photometric system, for example -- magnitude V . The difference mM AS S - V dep ends on the catalog color in different ways for different MASS sp ectral resp onses. As the problem is mainly related to the sp ectral region short-ward of 420 nm, the use of the m M AS S - B color instead mM AS S - V is preferable. The color equations calculated for all MASS resp onse curves are presented in Fig. 6. All functions are normalized to the A0 V sp ectral typ e. One can see that the slop e of these curves strongly dep ends 5


on the MASS resp onse. For the extreme cases mass dimm and eso md, the slop e varies from -0.64 to -0.19, dep ending mainly on the central wavelength 0 (see Table 1). The bandwidth affects the curvature of the color equation. For example, the color equation . for the eso md deviates down for white stars (B - V < 0 m0) since this band covers the part of stellar sp ectrum b efore the Bahlmer jump. Measurements of the B0 ­ F0 stars p ermit to estimate for a sp ecific MASS device. The comparison b etween the color equations for elt mass dimm and mass shows that these equations are coincident for B - V > 0m0. For B0 stars, mM AS S - B for these curves differ by only 0m08. . . It is not a large difference, therefore sp ecial measurements are needed for estimation.

0,2 0,0 -0,2 -0,4 -0,6 -0,8 -1,0

0,2 0,0 -0,2 -0,4 -0,6 -0,8 -1,0

-- B

MASS

m

mass mass_dimm without_cut without eso_md elt_mass_dimm

m

MASS

-- B

elt_mass_dimm measured 1-st measured 2-nd

0,0

0,5

B -- V

1,0

1,5

0,0

0,5

B -- V

1,0

1,5

Figure 6: On the left: The calculated color-color diagram m M AS S - B vs. B - V for all MASS sp ectral resp onse curves. On the right: The color equation for the elt mass dimm (line) and the measurements made with the ESO MASS/DIMM (p oints). The prop osed metho d involves the calculation of the color equation from the standard energy distributions. Therefore, the inaccuracies of the input data pro duce the color correction errors. As this correction can b e large, its errors can achieve 0 m03 or more for red stars. . The situation is complicated by the fact that ab out 30% stars in the MASS catalog are variable. Thus, among the 12 target stars measured at Tolar in 2004 ­ 2006, six stars are known to b e variable with amplitudes from 0m01 to 0m3. Moreover, the photometric data for bright stars are less accurate . . than for the fainter stars. However, the problem of establishing the sp ectral resp onse is simplified by the fact that the bandwidth and the central wavelength are strongly related. It is easy to see this in Fig. 6. This relation may b e slightly distorted by the additional cutoff in the red, as in the case of mass and without cut, but these cases are not problematic. A practical metho d of the sp ectral resp onse measurement is presented in the App endix.

Exp erimental tests.
The first sp ecial measurements were accomplished by M. Sarazin during the ESO MASS/DIMM tests at La Chira. On the nights of August 2 and 3, 2006, 12 sp ecially chosen stars were measured, for 5 ­ 10 minutes each. Note that among the 20 different stars selected from star.lst, 7 stars are susp ected variables.

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The preliminary data reduction included the magnitude correction to the zenith (not outside the atmosphere!) with the typical extinction co efficient of 0 m25. This value is an estimate only, but its . error is less than 0m05, leading to the zenith-magnitude error of less than 0 m02 at the maximum . . airmass of 1.34. Such pro cedure gives the resp onse curve which includes the atmospheric transmission comp onent. The restoration metho d presented in App endix could not b e applied due to the small amount of the measurements and the non-uniform coverage of the color range. The comparison of the instrumental colors m M AS S - V with the calculated color equation shows that the eso md curve adopted as a first approach did not agree with the measurements. To achieve the agreement, the blue cutoff of the resp onse was shifted to the red in several steps, until an agreement was reached. As result, the curve elt mass dimm was obtained. This curve should b e used with the ESO MASS-DIMM. Similar reduction was applied to the measurements obtained at Tolar in 2004 ­ 2006. In this case the extinction co efficient was determined from the data itself. It is found to b e in the range 0 m16 ­ . 0m20 (the sp ectral resp onse of this device is "redder" compared to the ESO device). Unfortunately, . these measurements did not contain stars of sufficiently different sp ectral typ es. Therefore, only the average slop e of the dep endence mM AS S - V vs. B - V was determined. These results for all the observational p erio d are presented in Fig. 7. On the right-hand side, the two histograms of the slop e (one for the p erio d b efore Octob er 2004, another after) are shown. To compute this dep endence for a given night, the measurements of a star and the next star were used if the difference b etween their B - V colors exceeded 0 m2 and the ro ot-mean-square flux deviation . did not exceed 0m01 for b oth. The latter condition guarantees the photometric sky quality, while the . first condition decreases the influence of the catalog magnitude errors.
1,0 0,8
(mMASS-V)/d(B-V)

40

30

0,6 20 0,4 0,2 0,0 10

n
3200 3400 3600 JD-2450000 3800 4000

0 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 d(mMASS-V)/d(B-V)

Figure 7: On the left: the slop e of the color equation for the MASS-DIMM at Tolar as a function of time (Julian date). On the right: the distribution of the slop es b efore Octob er 2004 (red, the median is 0.31) and after (blue, the median is 0.50) Since it is known that the multilayer re-imaging mirror are used in the Tolar device, we conclude what the device sp ectral resp onse matched the mass dimm curve b efore Octob er 2004 and the without cut curve after that date.

Conclusion
This study shows that in order to control or improve the knowledge of the MASS sp ectral resp onse and to avoid the turbulence profile bias caused by the p o or knowledge of the resp onse, a short sp ecial program of photometric measurements (one half night p er season) must b e included in the overall 7


schedule. A sp ecial list of the stars with brightness 4 m В 5m is needed for such measurements. Such . . stars have more precise catalog magnitudes than the normal (brighter) MASS targets. The numb er of stars must b e sufficient to exclude all susp ected variable stars and to optimize the distribution of the colors. During the program execution, the stars at airmass M z 1.0 will b e measured for the color equation and stars at Mz 1.6 will b e measured to define the extinction co efficient. The use of a supplementary cut-off filter with the b oundary at 380 nm will give a more reliable and precise result. In this approach, the difference b etween the fluxes with and without such filter will b e small and will b e measured with high accuracy. The catalog magnitudes are not needed at all. Unfortunately, this pro cedure can not b e carried out remotely. After finishing the measurements, the filter may b e left in the device in order to fix the blue cutoff and to eliminate the need of such measurements in the future. For the new devices, the installation of such filter is very desirable. The commercially available filter GG385 from Schott with thickness 3 mm and diameter 25 mm can b e obtained from http://www.pgoonline.com/intl/katalog/schott.html, for example. It is p ossible to insert the filter together with the Fabry lens.

A. Photometric band determination with minimal assumptions
The prop osed pro cedure uses the fact that unknown (or p o orly known) features of the sp ectral resp onse curve are asso ciated with its blue cut-off. The b ehavior of the sp ectral resp onse at the red side is defined by the sp ectral resp onse of the PMT and is considered as a priori known. The blue slop e of the resp onse is mo deled by a simple formula: s() = exp - ( - c ) r4
4

for < c ,

s() = 1 for c .

(1)

1,0 0,8

1,0 0,8

S()

0,6 0,4 0,2 0,0 300

S()
500 600 700

0,6 0,4 0,2 0,0 300

400

, nm

400

, nm

500

600

700

Figure 8: On left: the original curve elt mass dimm used to compute the simulated colors m M AS S - B (black) and a few resp onse curves restored from these colors with different noise realizations (red). On right: the same for without cut. The function under the exp onent is the dep endence of region. For most optical glasses, the absorption co efficient by the bi-quadratic function. The formula (1) gives the imp ortance b ecause the normalization will b e included in 8 the absorption co efficient on in the blue near its sharp growth is approximated well un-normalized dep endence, but it is of no the zero-p oint.


Hereafter the problem is reduced to the calculation of the 3-parameter dep endence C I = m M AS S - B on B - V , where the third parameter is the zero-p oint C I 0 which shifts the C I (c , r ) curve vertically. Using a minimization pro cedure, a set of the parameters that fits the measured instrumental colors can b e found. For the minimization, a C-mo dule pluggable into xmgrace was written, and the determination of the C I0 , c , r has b een accomplished with the help of Data/Transformation/Non-linear curve fitting function of xmgrace. In the absence of real data, I tested the metho d by numerical simulation. For the elt mass dimm curve, I calculated 12 p oints of the color equation m M AS S - B and added random noise with an amplitude of 0m02 to each p oint. The results of the parametric restoration are presented in Fig. 8. . One can see that the sp ectral resp onse was well restored. Note that the elt mass dimm curve was defined earlier by the iterative metho d, therefore it is not very well describ ed by (1). The simulation for the without cut curve with sharp details have b een done as well. The smo oth resp onse curve was obtained. The 0m02 noise do es not affect the restoration of the sp ectral resp onse. . However, when the noise is increased to 0 m05, the restoration b ecomes unstable. . A comparison b etween the WFs for the initial resp onse with the WF for the restored resp onse shows that in the first case the difference do es not exceed 2.5%, and in the second case it is less than 10%. The larger difference for the without cut curve is explained by its sp ecific shap e. This explains also why the restored values of 0 = 486 nm and = 106 nm differ from the true (input) values.

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