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Exposure Time Estimation for WFPC2 Images of Stellar Targets
-J. Biretta, 9 March 1995, v1.0
We describe how to estimate exposure times for point-source targets. In section (1) we show how to derive count rates using both analytic formulae and SYNPHOT. In section (2) we use these count rates to derive signal-to-noise ratios and exposure times. Section (3) discusses exposure splitting to eliminate cosmic rays, and section (4) gives several examples.
Contents:
1) Estimation of the detected count rate for the target.
A) Count rate estimation using WFPC Handbook
Equation 6.1.
B) Count rate estimation using SYNPHOT with
a blackbody approx.
C) Count rate estimation using SYNPHOT with
Gunn-Stryker Atlas.
2) Estimation of signal-to-noise ratios and exposure times
for target.
A) Detailed Signal-to-Noise Ratio (SNR) Calculation.
B) Exposure Time Estimation.
3) Cosmic Rays and Exposure Splitting.
4) Examples.
Appendix: Bruzual-Persson-Gunn-Stryker Spectrophotometric Atlas.
1) Estimation of the detected count rate for the target.
The most general situation will be one in which the target is a star for which the observer has a magnitude. Here we work out an example of an G5V star with V=20 observed in the F555W filter on CCD WF3. We use several methods; from quickest to most detailed, these are:
A) WFPC Handbook Equation 6.1, B) SYNPHOT black body approximation, and C) SYNPHOT Gunn-Stryker Atlas
Herein "Handbook" refers to the WFPC2 Instrument Handbook v.2.0.
A) Count rate estimation using WFP2 Handbook Equation 6.1
This is perhaps the quickest method of count rate estimation, and will be sufficient for most purposes. Equation 6.1 is:
s = 2.5x1011 * t * integral{QT d(lambda)/(lambda)}
* 10[-0.4(V+AB)] [eqn 1]
Where t = exposure time,
integral{} is tabulated as the second column of
Handbook Table 6.2
V = V magnitude of target
AB is tabulated in Handbook Table 6.1
For the example, the F555W filter has integral{} = 0.0291, and the G5V star has V=20 and AB~0.0. Hence the count rate is:
R = s / t = 2.5x1011 * 0.0291 * 10[-0.4(20+0.0)] R = 73 electrons sec-1.
B) Count rate estimation using SYNPHOT with a blackbody approximation.
SYNPHOT in the STSDAS package can be used to make a more detailed estimation of the target count rate. It will be more detailed in that the actual CCD can be specified, and the actual response curves of the CCD and filter are used.
For the observation mode (or "obsmode") we input "wfpc2,2,f555w" for the obsmode, to indicate wfpc2, camera 3 meaning CCD WF3, and the filter f555w.
For the target spectrum (or "spectrum) we use our knowledge that a G5V star can be approximated by a 5500 degree Kelvin blackbody. We input "rn(bb(5500),band(v),20.0,vegamag" which means to use a 5500 degree blackbody which is normalized to V=20 in a system where Vega is defined to have magnitude zero.
The output form in set to "counts" which here means detected electrons.
In detail the input dialog looks like this:
>cl
cl>stsdas
st>hst_calib
hs>synphot
epar calcphot
Image Reduction and Analysis Facility
PACKAGE = synphot
TASK = calcphot
obsmode = wfpc2,3,f555w Instrument observation mode
spectrum= rn(bb(5500),band(v),20.0,vegamag) Synthetic spectrum to calculate
form = counts Form for output data
(vzero = ) List of values for variable zero
(output = ) Output table name
(append = no) Append to existing table?
(result = 0.) Result of synphot calculation for form
(wavetab= ) Wavelength table name
(refdata= ) Reference data
(mode = h)
After typing the input parameters as shown above (using
Mode = band(wfpc2,3,f555w)
Pivot Equiv Gaussian
Wavelength FWHM
5440.531 1234.912 band(wfpc2,3,f555w)
Spectrum: rn(bb(5500),band(v),20.0,vegamag)
VZERO (COUNTS s^-1 hstarea^-1)
0. 81.24629
The result indicates that the target will have a countrate R = 81 electrons sec-1. This is slightly higher than the value given above, which largely reflects the high QE of CCD WF3.
C) Count rate estimation using SYNPHOT with Gunn-Stryker Spectrophotometic Atlas.
This is perhaps the most accurate count rate estimator, since actual stellar spectra are convolved with the CCD and filter response functions. While we illustrate a G5V star here, this will probably be most useful for very early or late spectral types, or UV wavelengths, where AB is significantly different from zero and difficult to interpolate.
Again, for the observation mode (or "obsmode") we input "wfpc2,2,f555w" for the obsmode, to indicate wfpc2, camera 3 meaning CCD WF3, and the filter f555w.
For the target spectrum we look in the paper by Gunn and Stryker, Ap.J.Supp 52, 121 (1983), and locate a G5V star in column 3 of their Table 1. (Or see Appendix 1 below.) We find that their star ID=44, HD 227547, is a G5V star. Hence we input to SYNPHOT the following specification for the "spectrum":
rn(crgridbpgs$bpgs_44.tab,band(v),20.0,vegamag)
Which tells synphot to use ID number 44 from the Gunn-Stryker Atlas, and to renormalize it to a magnitude of V=20.0 in a system where Vega has magnitude zero. We note that the actual spectra being used are from the Bruzual-Persson-Gunn-Stryker, where the original spectra are extended into the UV and IR.
Again, the output form in set to "counts" which here means detected electrons.
In detail the SYNPHOT input dialog looks like this:
>cl
cl>stsdas
st>hst_calib
hs>synphot
epar calcphot
Image Reduction and Analysis Facility
PACKAGE = synphot
TASK = calcphot
obsmode = wfpc2,3,f555w Instrument observation mode
spectrum= rn(crgridbpgs$bpgs_44.tab,band(v),20.0,vegamag) Synthetic spectrum to calculate
form = counts Form for output data
(vzero = ) List of values for variable zero
(output = ) Output table name
(append = no) Append to existing table?
(result = 0.) Result of synphot calculation for form
(wavetab= ) Wavelength table name
(refdata= ) Reference data
(mode = h)
After typing the input parameters as shown above (using
Mode = band(wfpc2,3,f555w)
Pivot Equiv Gaussian
Wavelength FWHM
5440.574 1234.956 band(wfpc2,3,f555w)
Spectrum: rn(crgridbpgs$bpgs_44.tab,band(v),20.0,vegamag)
VZERO (COUNTS s^-1 hstarea^-1)
0. 82.52274
The result indicates that the target will have a countrate R = 82.5 electrons sec-1. This is just slightly higher than the previous value assuming a blackbody spectrum.
2) Estimation of signal-to-noise ratio and exposure time.
The second part of exposure time estimation involves taking account of the various noise sources, estimating the signal- to-noise ratio (SNR), and finally computing the exposure time.
In section (A) below we outline a generalized SNR calculation including photon noise, read noise, dark noise, and sky noise. Section (B) presents a similar calculation for exposure time. Proposers interested only in rough exposure time estimates should go directly to section (B) equations 13 to 15.
A) Detailed Signal-to-Noise Ratio (SNR) Calculation.
There are several noise sources, which we now consider - photon noise of the target, and three sources of "background" noise: read noise of the CCD, noise from the dark current, and photon noise from the sky.
i) Target photon noise. The noise due to the target is simply:
n(target) = sqrt(R * t) [eqn 2]
where R is the target count rate, and t is the exposure time.
ii) CCD read noise. This is independent of exposure time and is approximately 5.3 electrons for the 7 electrons per DN gains setting (default), and 7.5 electrons for the 14 gain setting. These values will be sufficiently accurate for most purposes; specific values for each CCD can be found in Handbook Table 4.3. Assuming the default gain setting of 7, we have:
n(read) = 5.3 [eqn 3]
iii) Dark current. The dark current acts as an additional source of "photons" with a corresponding noise. The dark current count depends on both the exposure time and camera overheads times, and is roughly:
d = DCR * (t+44) = 0.003 * (t+44)
at the standard CCD operating temperature of -88 (-90 nominal) degrees C. (See Handbook Table 4.4 for values at other CCD temperatures.) Note DCR = dark count rate in electrons sec-1. The noise will be just the square root of these counts:
n(dark) = sqrt(0.003 * (t+60)) [eqn 4]
iv) Noise from Sky Counts. The counts contributed by sky glow depend on the target location in the sky. See Handbook Table 6.3. For example, a target near the ecliptic pole suffers a sky glow of V=23.3 mag. per square arcsecond, or converting to WFC pixels by adding 5 magnitudes (or 6.7 for PC), the sky brightness is 23.3+5=28.3 mag. per WFC pixel. For targets near the ecliptic, the sky brightens by about 1 magnitude. Using Handbook Equation 6.1 and Tables 6.1 and 6.1, the sky contributes a count rate:
SCR = 2.5x1011 * integral{QT d(lambda)/(lambda)} * 10[-0.4(V+AB)]
For example, in F555W at the ecliptic pole we have:
SCR = 2.5x1011 * 0.029 * 10[-0.4(28.3+0)]
= 0.0347
where SCR = the Sky Count Rate per pixel, integral{QT d(lambda)/(lambda)} = 0.029 is from Table 6.2 for the F555W filter, V=28.3 mag from above, and AB=0 for the sky from Table 6.1. For convenience, we have tabulated values of the Sky Count Rate (SCR) in Table 1 for most broadband filters.
Table 1. Sky Count Rates (SCR, electrons per sec.
per pixel) for targets at the ecliptic pole. For targets
near ecliptic plane, multiply by 2.5.
Filter WFC PC
------- ------ ------
F336W 0.0006 0.0001
F439W 0.0034 0.0007
F547M 0.0146 0.0029
F555W 0.035 0.0068
F569W 0.027 0.0054
F606W 0.059 0.0122
F622W 0.039 0.0081
F675W 0.037 0.0077
F702W 0.055 0.0011
F785LP 0.016 0.0033
F791W 0.032 0.0066
F814W 0.036 0.0075
F850LP 0.0079 0.0016
The noise contributed by the sky is again merely the square root of the total counts, or:
n(sky) = sqrt(SCR * t) [eqn 5]
Both the read noise, the dark noise, and the sky noise all act effectively as background noises per pixel, and may be summed as:
n(background) = sqrt( n(read)2 + n(dark)2 + n(sky)2 ) [eqn 6]
= sqrt( 5.32 + 0.003*(t+44) + SCR*t )
The contribution to the total noise will depend upon the number of pixels in the PSF, and how pixels in the PSF are weighted during data reduction. The number of pixels depends on the camera (PC or WFC), the wavelength, and where the PSF lands on the pixel grid. If it the target lands in the middle of a pixel, the number of pixels in PSF is minimized. If it lands in a pixel corner the number of pixels is maximized. Here we will assume the PSF pixels are weighed in proportion to their intensity, which maximizes the signal-to-noise ratio.
The total noise due to these "background" sources is thus:
n(total background) = sqrt[effective number of pixels] * n(background)
= n(background) / sqrt[sharpness] [eqn 7]
where n(background) is the noise per pixel from all "background" sources, and [sharpness] is the reciprocal of the effective number of pixels in the PSF. Values for the [sharpness] parameter are tabulated in WFPC2 Handbook Table 6.4 for optimal weighting of the PSF pixels. We note the "Obs." or observed values should be used. For the Wide-Field Camera (WFC) we may take [sharpness]=0.10 to reasonably good approximation at all wavelengths, with a bias towards computing a minimum signal-to-noise ratio for all target positions. For the Planetary Camera (PC) [sharpness]=0.045 is a similar single-value compromise. (Note that if aperture photometry is used to analyze that data, it will be more appropriate to set [sharpness] to the reciprocal of the number of pixels in the aperture.)
The total noise, combining the target photon noise and the total background noises, is thus:
n(total) = sqrt( n(photon)2 + n(background)2/[sharpness] ) [eqn 8]
and the signal-to-noise ratio is:
SNR = r * t / n(total) [eqn 9].
Combining equations 2 through 9, the signal to noise ratio is thus:
R*t
SNR = ------------------------------------------------ [eqn 10]
( n(read)2 + DCR*(t+44) + SCR*t )
sqrt( R*t + -------------------------------- )
( [sharpness] )
where R = target count rate (electrons sec-1; from section 1 above),
t = exposure time (sec.),
n(read) = read noise (electrons pixel-1; Handbook Table 4.3),
DCR = dark count rate (electrons sec-1 pixel-1; Handbook Table 4.4),
SCR = sky count rate (electrons sec-1 pixel-1; above Table 1),
[sharpness] = PSF sharpness (Handbook Table 6.4)
Using typical values n(read)=5.3, DCR=0.003, and [sharpness]=0.10 (WFC) or 0.045 (PC) described above, this may be simplified to:
R*t
SNR(WFC) = ------------------------------------ [eqn 11]
sqrt( 282 + (0.030 + 10*SCR + R)*t )
R*t
SNR(PC) = ------------------------------------ [eqn 12]
sqrt( 622 + (0.067 + 22*SCR + R)*t )
where SNR is the signal-to-noise ratio for the WFC and PC, respectively,
R = target count rate (electrons sec-1; from section 1 above),
t = exposure time (sec.), and
SCR = sky count rate (electrons sec-1 pixel-1; above Table 1).
B) Exposure Time Estimation.
Since we are really interested in knowning the exposure time, t, it is useful to solve the quadratic equation [eqn 10]. We find:
1
t = ----- ( B + sqrt[ B2 + 4 * A * Y ] ) [eqn 13]
2*Y
where:
n(read)2 + 44 * DCR
A = ----------------------
[sharpness]
DCR + SCR
B = ----------- + R
[sharpness]
Y = ( R/SNR )2
and t = exposure time (sec.),
SNR = desired signal-to-noise ratio,
R = target count rate (electrons sec-1; from section 1 above),
n(read) = read noise (electrons pixel-1; Handbook Table 4.3),
DCR = dark count rate (electrons sec-1 pixel-1; Handbook Table 4.4),
SCR = sky count rate (electrons sec-1 pixel-1; above Table 1),
[sharpness] = PSF sharpness (Handbook Table 6.4).
We note that A is in effect the square of the time-independent noise, while B*t is the square of the Poisson noise.
Using typical values n(read)=5.3, DCR=0.003, and [sharpness]=0.10 or 0.045, we find for the Wide Field Camera (WFC):
A = 282, B = 0.030 + 10*SCR + R [eqn 14]
and for the Planetary Camera (PC):
A = 622, B = 0.067 + 22*SCR + R. [eqn 15]
For example, if we want a signal-to-noise ratio (SNR)=100 for the example target in section 1 with R=81 counts sec.-1 in the WFC and filter F555W, we have:
A = 282 B = 0.030 + 10*(0.035) + 81 = 81.38 Y = ( 81/100 )2 = 0.656
and an exposure time:
1
t = ------- ( 81.38 + sqrt[ 81.382 + 4 * 282 * 0.656] )
2*0.656
t = 127 sec.
WFPC2 allows only certain discrete exposure times, which are listed in Handbook Table 2.3. We note that the next larger allowed exposure is 140 sec., so we would request:
t = 140 sec.
3) Cosmic Rays and Exposure Splitting
An additional consideration when choosing exposures is the cosmic ray flux on the detector. Cosmic rays corrupt approximately 20 pixels per second on each CCD. These artifacts can be removed by spliting exposures into two or more sub-exposures, so as to allow removal of corrupted pixels in the combined image.
The impact of cosmic rays, and the recommended spliting, depends on the science goals. Programs seeking to image a small target (a few arcseconds in size) will tend to be relatively robust against cosmic rays. Whereas programs searching for faint objects over a wide area are more susceptible to cosmic ray artifacts. Below we give rough guidelines for the number of sub-exposures required for a given total exposure.
We also note that splitting exposures will increase the total noise as sqrt(number of sub-exposures) if the read noise dominates. The read noise will dominate in cases where A >> B*t in equations 13 to 15 above. In these cases some iteration maybe needed to determine the correct total exposure and number of sub-exposures to produce a desired signal-to-noise ratio. Splitting will have little impact on the noise if the observation is limited by Poisson noise from the target or sky (A << B*t).
Table 2. Recommended Number of Sub-Exposures
Total Exposure Recommended Number of Sub-Exposures
Time (sec.)
Robust Programs Search Programs
-------------- --------------- ---------------
0-300 2 3
300-600 2 4
600-1600 3 4
1600-5000 3 5
5000-10000 4 6
>10000 one exp. per orbit one exp. per orbit
These values were estimated under the assumption that a 1% probability of irrecoverable damage to a 1 arcsec. square target was acceptable for "robust programs." But only 0.01 corrupted pixels per CCD was acceptible in the combined image for "search programs."
We note that the telescope scheduling software automatically splits all exposures longer that 600 sec. into two sub-exposures, unless CR-SPLIT=NO is specified.
In general, it will be advantageous to dither the pointing of the split exposures by integral pixels, so as to aid in removal of hot pixels. For the PC a dither of POS TARG 0.501, 0.501 arcec. is recommended; on the WFC we recommend 0.498, 0.498 arcsec. See memos elsewhere on dithering.
4) Examples:
A) Target is a M6V star with I=19.5 which is to be observed in CCD WF2 in F336W. A signal-to-noise ratio of 30 is needed. Target is near ecliptic pole.
First we derive the count rate using Handbook equation 6.1 and Tables 6.1 and 6.2:
R = 2.5x1011 * integral{QT d(lambda)/(lambda)} * 10[-0.4(V+AB)]
= 2.5x1011 * 0.00425 * 10[-0.4(19.5+7)]
= 0.027
Alternatively, we may derived the count rate with SYNPHOT. SYNPHOT is likely to be more accurate since we donot need a large extrapolation to get AB in Table 6.2.
From Appendix 1 we see that star ID=69 is an M6V star. We use SYNPHOT to compute the count rate. We specify "spectrum" such that the Atlas spectrum will be normalized to I=19.5.
The inputs to SYNPHOT are:
Image Reduction and Analysis Facility
PACKAGE = synphot
TASK = calcphot
obsmode = wfpc2,2,f336w Instrument observation mode
spectrum= rn(crgridbpgs$bpgs_69.tab,band(i),19.5,vegamag) Synthetic spectrum to
form = counts Form for output data
(vzero = ) List of values for variable zero
(output = ) Output table name
(append = no) Append to existing table?
(result = 0.) Result of synphot calculation for form
(wavetab= ) Wavelength table name
(refdata= ) Reference data
(mode = h)
SYNPHOT outputs:
Mode = band(wfpc2,2,f336w)
Pivot Equiv Gaussian
Wavelength FWHM
3338.881 471.4442 band(wfpc2,2,f336w)
Spectrum: rn(crgridbpgs$bpgs_69.tab,band(i),19.5,vegamag)
VZERO (COUNTS s^-1 hstarea^-1)
0. 0.034795
Using equation 13 and 14, we set R=0.0348, SNR=30, so that:
Y = (0.0348/30)2 = 1.346E-6 A = 282
From Table 1 above we see SCR=0.0006. Hence
B = 0.030 + 10*SCR + R = 0.030 + 10*0.0006 + 0.0348 = 0.0708
and the exposure time is:
1
t = ----- ( B + sqrt[ B2 + 4 * A * Y ] )
2*Y
1
t = ----------- ( 0.0708 + sqrt[ 0.07082 + 4 * 282 * 1.346E-6 ] )
2*1.346E-6
t = 56000 sec.
From Table 2 we see that this should be split into separate one-orbit exposures. For a typical visibility period of ~45 minutes this means twentyfour 2400 sec. exposures. Since A << Bt (i.e. 282 << 4000) we are Poisson noise limited, and no exposure time adjustment is needed to compensate for the exposure splitting. As it turns out, the dominant noise source is the Poisson noise of the target and dark current.
B) Target is an K3III star with V=29 which is to be observed in CCD WF3 in F606W. A signal-to-noise ratio of 10 is needed. Target is near ecliptic pole.
From Appendix 1 we see that star ID=143 is a K3III star. We use SYNPHOT to compute the count rate. We specify "spectrum" such that the Atlas spectrum will be normalized to V=29.
SYNPHOT input:
PACKAGE = synphot
TASK = calcphot
obsmode = wfpc2,3,f606w Instrument observation mode
spectrum= rn(crgridbpgs$bpgs_143.tab,band(v),29.,vegamag) Synthetic spectrum to
form = counts Form for output data
(vzero = ) List of values for variable zero
(output = ) Output table name
(append = no) Append to existing table?
(result = 0.) Result of synphot calculation for form
(wavetab= ) Wavelength table name
(refdata= ) Reference data
(mode = h)
SYNPHOT output:
Mode = band(wfpc2,3,f606w)
Pivot Equiv Gaussian
Wavelength FWHM
5998.75 1503.804 band(wfpc2,3,f606w)
Spectrum: rn(crgridbpgs$bpgs_143.tab,band(v),29.,vegamag)
VZERO (COUNTS s^-1 hstarea^-1)
0. 0.041766
Using equation 13 and 14, we set R=0.0418, SNR=10, so that:
Y = (0.0418/10)2 = 1.747E-5 A = 282
From Table 1 above we see SCR=0.059. Hence:
B = 0.030 + 10*SCR + R = 0.030 + 10 * 0.059 + 0.0418 = 0.6618
and the exposure time is:
1
t = ----- ( B + sqrt[ B2 + 4 * A * Y ] )
2*Y
1
t = ----------- ( 0.6618 + sqrt[ 0.66182 + 4 * 282 * 1.747E-5 ] )
2*1.747E-5
t = 38000 sec.
From Table 2 we see that this should be split into sixteen single-orbit exposures. Since A << Bt (i.e. 282 << 25000) the Poisson noise dominates and no exposure adjustment is needed due to splitting.
C) Target is an K3III star with V=16 which is to be observed in PC1 in F1042M. A signal-to-noise ratio of 10 is needed. Target is near ecliptic pole.
From Appendix 1 we see that star ID=143 is a M3III star. We use SYNPHOT to compute the count rate. We specify "spectrum" such that the Atlas spectrum will be normalized to V=16.
SYNPHOT input:
PACKAGE = synphot
TASK = calcphot
obsmode = wfpc2,3,f1042m Instrument observation mode
spectrum= rn(crgridbpgs$bpgs_143.tab,band(v),16.,vegamag) Synthetic spectrum to
form = counts Form for output data
(vzero = ) List of values for variable zero
(output = ) Output table name
(append = no) Append to existing table?
(result = 0.) Result of synphot calculation for form
(wavetab= ) Wavelength table name
(refdata= ) Reference data
(mode = h)
SYNPHOT output:
Mode = band(wfpc2,3,f1042m)
Pivot Equiv Gaussian
Wavelength FWHM
10224.94 639.1379 band(wfpc2,3,f1042m)
Spectrum: rn(crgridbpgs$bpgs_143.tab,band(v),16.,vegamag)
VZERO (COUNTS s^-1 hstarea^-1)
0. 45.77681
Using equation 13 and 15 (for PC), we set R=45.8, SNR=10, so that:
Y = (0.0418/10)2 = 20.98 A = 622
The F1042M filter is not listed in Table 1; its sky count rate in negligible so we set SCR=0. Hence:
B = 0.067 + 22*SCR + R = 0.067 + 22 * 0 + 45.8 = 45.8
and the exposure time is:
1
t = ----- ( B + sqrt[ B2 + 4 * A * Y ] )
2*Y
1
= ----------- ( 45.8 + sqrt[ 45.82 + 4 * 622 * 20.98 ] )
2*20.98
t = 6.6 sec.
It is unlikely that a star in such short exposure would be impacted by cosmic rays. Nonetheless, if we did decide to split it into two exposures, we note that A >> Bt (i.e. 622 >> 300) so that the read noise dominates. Hence, the exposure should be increased by sqrt(2) to compensate for the splitting; two 5 sec. exposures would be made.
Appendix
Appendix 1. Directory of Stars in Bruzual-Persson-Gunn-Stryker Spectrophotometric Atlas.
ID STAR NAME SP T AV V U-B B-V V-R R-I V-K 1 9 SGR O5 1.120 4.794 -1.150 -0.337 -0.397 -0.437 -0.930 2 9 SGE O8F 1.010 5.264 -1.114 -0.323 -0.385 -0.475 -0.930 3 HR 8023 O6 1.140 4.829 -1.083 -0.313 -0.393 -0.472 -0.930 4 -1 935 B1V 0.218 4.961 -0.955 -0.263 -0.342 -0.398 -0.810 5 60 CYG B1V 0.170 5.277 -0.911 -0.269 -0.369 -0.435 -0.850 6 102 HER B2V 0.250 4.007 -0.831 -0.245 -0.360 -0.447 -0.740 7 ETA HYA B3V 0.030 4.134 -0.684 -0.201 -0.312 -0.347 -0.610 8 IOTA HER B3V 0.075 3.685 -0.665 -0.203 -0.323 -0.380 -0.610 9 HR 7899 B4V 0.070 5.831 -0.652 -0.195 -0.340 -0.386 -0.570 10 38 OPH A1V 0.510 5.351 -0.490 -0.139 -0.293 -0.330 -0.380 11 HR 7174 B6V -0.060 5.977 -0.287 -0.107 -0.255 -0.306 -0.280 12 9 VUL B7V -0.080 5.147 -0.283 -0.099 -0.254 -0.273 -0.240 13 HD 189689 B9V 0.090 7.203 -0.228 -0.081 -0.251 -0.250 -0.180 14 THETA VIR A0V 0.030 4.278 0.150 -0.026 -0.210 -0.222 -0.060 15 NU CAP B9V -0.060 4.843 0.052 -0.020 -0.211 -0.213 -0.040 16 HR 6169 A2V 0.067 6.373 0.177 -0.017 -0.203 -0.246 -0.040 17 HD 190849A A1V 0.300 6.825 0.113 0.009 -0.219 -0.215 0.020 18 69 HER A2V 0.032 4.561 0.167 0.000 -0.203 -0.235 0.000 19 HD 190849B A3V 0.300 7.271 0.180 0.057 -0.194 -0.196 0.150 20 58 AQL A0V 0.056 5.534 0.193 0.057 -0.170 -0.168 0.150 21 78 HER B9V -0.290 5.972 0.215 0.036 -0.170 -0.190 0.100 22 HR 6570 A7V 0.039 6.001 0.262 0.107 -0.165 -0.209 0.290 23 HD 187754 A2V 0.110 8.365 0.343 0.125 -0.131 -0.114 0.360 24 THETA1 SER A5V 0.026 4.554 0.225 0.143 -0.120 -0.153 0.400 25 PRAESEPE 276 0.007 7.558 0.317 0.159 -0.091 -0.132 0.420 26 PRAESEPE 114 0.007 8.223 0.255 0.175 -0.074 -0.117 0.460 27 PRAESEPE 154 0.086 8.399 0.207 0.219 -0.065 -0.093 0.560 28 HD 190192 A5V 0.155 8.507 0.216 0.231 -0.048 -0.083 0.610 29 PRAESEPE 226 0.086 8.801 0.180 0.275 -0.012 -0.052 0.720 30 PRAESEPE 37 0.086 8.906 0.155 0.306 0.010 -0.053 0.810 31 HD 191177 F4V 0.099 8.731 0.220 0.309 0.035 -0.047 0.840 32 PRAESEPE 332 0.086 9.617 0.079 0.389 0.070 -0.008 1.010 33 BD+293891 F6V 0.092 9.085 0.114 0.398 0.098 0.000 1.040 34 PRAESEPE 222 0.086 10.016 0.089 0.430 0.096 0.031 1.110 35 HD 35296 F8V 0.010 4.833 0.100 0.489 0.157 0.059 1.210 36 BD+263780 G0V 0.045 8.433 0.088 0.503 0.164 0.053 1.240 37 HD 148816 F9V 0.028 7.257 -0.030 0.509 0.179 0.093 1.260 38 HD 155675 F8V 0.051 8.427 0.042 0.508 0.186 0.090 1.260 39 PRAESEPE 418 0.087 10.482 0.144 0.527 0.160 0.059 1.270 40 HYAD 1 0.027 7.345 0.196 0.530 0.169 0.066 1.270 41 HD 122693 F8V 0.040 7.999 0.207 0.511 0.194 0.043 1.250 42 HD 154417 F8V 0.017 5.941 0.131 0.538 0.181 0.058 1.290 43 HYAD 2 0.027 7.715 0.223 0.579 0.194 0.072 1.380 44 HD 227547 G5V 0.062 9.843 0.230 0.589 0.201 0.089 1.400 45 HD 154760 G2V 0.041 8.639 0.204 0.586 0.211 0.096 1.390 46 HD 190605 G2V 0.027 7.639 0.283 0.593 0.204 0.078 1.400 47 HYAD 15 0.027 8.014 0.285 0.620 0.223 0.105 1.470 48 HD 139777A K0V 0.010 6.637 0.204 0.631 0.244 0.094 1.490 49 HD 136274 G8V 0.020 7.849 0.410 0.672 0.283 0.123 1.550 50 HYAD 26 0.028 8.559 0.407 0.710 0.259 0.115 1.620 51 HD 150205 G5V 0.021 7.468 0.383 0.700 0.257 0.141 1.620 52 HYAD 21 0.028 9.060 0.536 0.766 0.282 0.152 1.780 53 +02 3001 G8V 0.017 7.448 0.470 0.789 0.365 0.175 1.840 54 HD 190571 G8V 0.017 7.430 0.587 0.816 0.338 0.200 1.950 55 HYAD 183 0.027 9.636 0.778 0.887 0.390 0.216 2.150 56 HD 190470 K3V 0.013 7.820 0.810 0.895 0.389 0.202 2.170 57 HD 154712 K4V 0.016 8.623 0.987 0.967 0.491 0.268 2.390 58 HYAD 185 0.027 9.410 0.999 1.074 0.548 0.341 2.680 59 +38 2457 K8V 0.012 9.773 1.170 1.057 0.555 0.272 2.600 60 HYAD 173 0.027 10.389 1.302 1.202 0.650 0.407 3.030 61 GL 40 M0V 0.008 8.860 1.305 1.269 0.756 0.475 3.260 62 HYAD 189 0.027 11.027 1.387 1.319 0.749 0.488 3.400 63 HD 151288 K7V 0.007 8.031 1.344 1.350 0.764 0.504 3.520 64 HD 157881 K7V 0.005 7.508 1.370 1.332 0.791 0.525 3.470 65 HD 132683 M0V 0.009 9.347 1.378 1.342 0.829 0.524 3.500 66 GL 15A M0V 0.005 8.030 1.331 1.514 1.057 0.812 4.030 67 GL 49 M2V 0.005 9.458 1.336 1.443 1.056 0.832 4.160 68 GL 109 M4V 0.005 10.490 1.380 1.501 1.233 1.044 4.620 69 GL 15B M6V 0.004 11.002 1.574 1.707 1.463 1.221 5.040 70 GL 83.1 M8V 0.005 12.235 1.450 1.704 1.674 1.404 5.580 71 GL 65 M5V 0.009 11.999 1.223 1.768 2.082 1.741 6.670 72 HR 7567 B1IV 0.640 5.142 -0.861 -0.249 -0.380 -0.443 -0.780 73 HR 7591 B2III 0.130 5.835 -0.844 -0.249 -0.343 -0.407 -0.780 74 20 AQL B3IV 0.670 4.471 -0.542 -0.156 -0.306 -0.340 -0.440 75 HR 7467 B3III 0.130 6.481 -0.569 -0.182 -0.318 -0.372 -0.540 76 IOTA LYR B7IV 0.030 5.390 -0.417 -0.132 -0.282 -0.308 -0.380 77 HR 7346 B7III -0.050 6.431 -0.288 -0.108 -0.269 -0.297 -0.280 78 59 HER A3III 0.067 5.357 0.200 -0.045 -0.239 -0.238 -0.100 79 HR 6642 A0IV 0.090 6.031 0.066 -0.041 -0.249 -0.268 -0.080 80 11 SGE B9IV -0.040 5.832 0.033 -0.027 -0.228 -0.264 -0.060 81 60 HER A3IV 0.041 4.780 0.227 0.085 -0.156 -0.186 0.240 82 HD 192285 A4IV 0.174 7.963 0.239 0.124 -0.144 -0.142 0.360 83 ALPHA OPH A5III 0.014 2.035 0.239 0.152 -0.108 -0.149 0.420 84 HD 165475B A5IV 0.085 7.478 0.317 0.229 -0.078 -0.123 0.590 85 HD 165475 A5IV 0.071 7.072 0.256 0.245 0.001 -0.026 0.650 86 XI SER F0IV 0.015 3.487 0.257 0.240 -0.040 -0.081 0.640 87 HD 5132 F0IV 0.064 7.559 0.182 0.287 -0.003 -0.082 0.740 88 HD 508 A9IV 0.124 8.115 0.279 0.305 0.001 -0.049 0.810 89 HD 210875 F0IV 0.149 8.523 0.302 0.317 -0.020 -0.050 0.860 90 RHO CAP F2IV 0.025 4.709 0.137 0.339 0.049 -0.017 0.930 91 HD 7331 F7IV 0.080 7.156 0.125 0.427 0.083 -0.004 1.090 92 BD+630013 F5IV 0.159 8.664 0.096 0.444 0.082 0.011 1.140 93 HD 13391 G2IV 0.095 8.531 0.180 0.546 0.194 0.049 1.300 94 HD 154962 G8IV 0.031 6.228 0.365 0.644 0.226 0.110 1.500 95 HD 192344 G4IV 0.059 7.671 0.368 0.646 0.218 0.113 1.500 96 HR 6516 G6IV 0.021 5.270 0.375 0.651 0.217 0.077 1.510 97 HR 7670 G6IV 0.026 5.718 0.478 0.672 0.229 0.079 1.510 98 HD 128428 G3IV 0.055 7.647 0.503 0.715 0.262 0.121 1.650 99 31 AQL G8IV 0.019 5.128 0.482 0.732 0.273 0.093 1.660 100 -02 4018 G5IV 0.080 8.595 0.583 0.791 0.353 0.153 1.850 101 M67 F143? 0.144 11.203 0.624 0.807 0.343 0.156 1.890 102 HD 11004 G5IV 0.073 7.951 0.532 0.825 0.389 0.242 1.970 103 HD 173399A G5IV 0.048 7.196 0.613 0.808 0.331 0.213 1.920 104 HD 56176 G7IV 0.031 6.233 0.629 0.857 0.364 0.230 2.010 105 HD 227693 G5IV 0.125 9.043 0.740 0.868 0.352 0.207 2.030 106 HD 199580 K2IV 0.052 7.136 0.835 0.881 0.385 0.206 2.080 107 HD 152306 G8III 0.090 6.923 0.695 0.880 0.355 0.169 2.060 108 PRAESEPE 212 0.084 6.451 0.837 0.894 0.361 0.208 2.100 109 THETA1 TAU G8III 0.027 3.694 0.872 0.904 0.366 0.219 2.120 110 HD 170527 G5IV 0.040 6.713 0.789 0.918 0.390 0.233 2.160 111 HD 136366 K0III 0.072 6.090 0.930 0.931 0.373 0.243 2.200 112 HD 191615 G8IV 0.061 7.708 0.890 0.947 0.422 0.258 2.210 113 HD 124679 K0III 0.045 5.112 0.893 0.946 0.383 0.221 2.210 114 HD 131111 K0III 0.049 5.336 0.939 0.956 0.428 0.282 2.250 115 HD 113439 K0III 0.070 7.143 1.045 0.957 0.421 0.206 2.230 116 HD 4744 G8IV 0.055 7.498 0.876 0.989 0.472 0.290 2.350 117 HD 7010 K0IV 0.071 8.006 0.904 0.994 0.453 0.270 2.320 118 46 L MI K0III 0.025 3.672 1.033 0.991 0.447 0.263 2.320 119 91 AQR K0III 0.031 4.130 1.123 1.010 0.440 0.253 2.360 120 M67 F141 0.145 10.196 1.144 1.007 0.431 0.226 2.350 121 HR 8924A K3III 0.073 6.104 1.253 1.015 0.417 0.229 2.350 122 HD 140301 K0IV 0.031 6.269 1.164 1.016 0.438 0.280 2.380 123 HD 95272 K0III 0.030 3.964 1.107 1.041 0.453 0.292 2.440 124 HD 72184 K2III 0.061 5.670 1.245 1.051 0.431 0.266 2.450 125 HD 119425 K2III 0.046 5.179 1.167 1.042 0.441 0.254 2.420 126 HD 106760 K1III 0.040 4.850 1.196 1.074 0.473 0.277 2.510 127 PSI U MA K1III 0.018 2.861 1.244 1.081 0.479 0.289 2.520 128 PHI SER K1III 0.054 5.448 1.308 1.067 0.400 0.242 2.480 129 HD 136514 K3III 0.065 5.303 1.442 1.105 0.461 0.289 2.570 130 MU AQL K3III 0.050 4.355 1.366 1.123 0.484 0.266 2.600 131 HR 5227 K2IIIP 0.067 6.168 1.364 1.146 0.511 0.293 2.650 132 HD 154759 K3III 0.122 8.093 1.413 1.172 0.543 0.288 2.720 133 20 CYG K3III 0.064 4.931 1.690 1.198 0.473 0.292 2.760 134 ALPH SER K2III 0.015 2.508 1.360 1.097 0.469 0.297 2.550 135 MU LEO K2III 0.026 3.733 1.520 1.172 0.520 0.301 2.730 136 +1 3131 K0III 0.076 6.402 1.203 1.143 0.520 0.312 2.660 137 M67 F170 0.144 9.415 1.662 1.237 0.585 0.340 2.870 138 18 LIB A K2IIIP 0.060 5.726 1.525 1.189 0.519 0.352 2.600 139 +28 2165 K1IV 0.073 9.557 1.642 1.259 0.614 0.358 2.950 140 NGC 188 1_69 0.100 12.229 1.544 1.232 0.568 0.383 2.900 141 +30 2344 K3III 0.077 10.239 1.691 1.263 0.630 0.373 2.950 142 HD 83618 K3III 0.037 3.741 1.550 1.262 0.602 0.387 2.960 143 HD 158885 K3III 0.144 7.025 1.522 1.260 0.600 0.420 2.970 144 HD 166780 K5III 0.138 7.188 1.791 1.323 0.652 0.422 3.120 145 HD 148513 K4III 0.074 5.260 1.939 1.386 0.591 0.426 3.310 146 M67 T626 0.144 9.107 1.858 1.391 0.672 0.433 3.310 147 HD 127227 K5III 0.084 7.298 1.999 1.389 0.739 0.481 3.320 148 M67 IV-202 0.146 8.533 2.070 1.463 0.777 0.512 3.480 149 HD 50778 K4III 0.044 3.888 1.846 1.384 0.707 0.523 3.310 150 HD 62721 K5III 0.067 4.650 1.868 1.393 0.730 0.529 3.340 151 HD 116870 M0III 0.069 5.097 1.896 1.413 0.776 0.571 3.410 152 HD 60522 M0III 0.049 3.844 2.037 1.482 0.803 0.602 3.680 153 -1 3113 K5III 0.125 8.161 2.334 1.609 0.860 0.609 3.790 154 +2 2884 K5III 0.090 6.623 2.046 1.434 0.838 0.629 3.550 155 -2 3873 M0III 0.096 6.906 2.135 1.549 1.060 0.850 4.320 156 HD 104216 M2III 0.097 5.972 1.935 1.523 1.037 0.872 4.300 157 HD 142804 M1III 0.121 6.386 2.309 1.694 1.023 0.907 4.280 158 HD 30959 M3III 0.065 4.469 2.142 1.705 1.297 1.064 4.860 159 HD 151658 M2III 0.194 7.212 2.305 1.770 1.361 1.119 5.000 160 -2 4025 M2III 0.120 8.843 2.038 1.643 1.420 1.195 5.180 161 -01 3097 M2III 0.125 9.038 2.058 1.612 1.510 1.279 5.300 162 TX DRA 0.112 7.049 1.885 1.547 1.525 1.339 5.400 163 Z CYG M8III 0.305 8.246 1.881 1.569 1.615 1.358 5.540 164 +01 3133 M5III 0.120 8.944 1.713 1.498 1.774 1.506 5.820 165 -2 3886 M5III 0.102 9.021 1.615 1.544 1.927 1.583 6.060 166 W HER M6III 0.115 10.578 0.818 1.099 2.562 1.959 7.000 167 TY DRA M8 0.144 8.777 1.267 1.564 2.347 1.969 6.740 168 SW VIR M7III 0.087 6.948 1.009 1.674 2.779 2.110 7.350 169 RZ HER M6III 0.310 12.767 0.126 1.380 3.068 2.397 7.000 170 R LEO 0.110 8.861 0.315 1.918 3.672 2.789 7.000 171 AW CYG N 0.324 8.215 2.614 3.790 1.650 0.956 7.000 172 WZ CAS N 0.327 6.535 3.579 2.636 1.397 1.073 7.000 173 69 CYG B0IB 0.442 5.511 -1.028 -0.234 -0.370 -0.395 -0.600 174 HR 7699 B5IB 1.051 5.167 -0.585 -0.190 -0.320 -0.376 -0.450 175 HR 8020 B8IA 1.333 4.395 -0.552 0.027 -0.153 -0.196 0.160