DSLR astrometry and photometry

 

Updated 2017 January 16

 

Contents

 

1.0 Introduction

 

1.1 Objectives

 

Please note that various program settings may be specific to my set-up and might vary for different telescope-camera combinations. The information used to assemble this tutorial was gleaned from a number of sources and took several months to come by. The tutorial may seem lengthy but I felt it better to have everything I have learned in one place.

 

It is still a work-in-progress but I feel quite confident that it is moving in the right direction.

 

The objectives of this tutorial are to explain how DSLR images can be used for astrometry and photometry of comets and asteroids. It will cover;

- using a DSLR camera attached to a refractor

- DSLR linearity check

- obtaining images

- taking calibration frames

- converting the images from RAW to FITS format and splitting out the green, blue and

   red channels

- calibrating images

- stacking

- astrometry

- photometry

 

1.2 Intermediate conclusion

 

Analysing a 20 sec image using Astrometrica and UCAC4/APASS V mags

- Astrometry within +/- 0.2 arc sec and therefore satisfactory

- Photometry within +/- 0.06 mag (+/- 0.03 using colour transformation)

 

2.0 DSLR Cameras

 

2.1 Canon EOS550D DSLR settings

 

The following settings have been gleaned from a number of sources and some are specific to using the camera for astrometry and photometry.

 

- set Mode dial to Manual                                                  EOS Manual P20

- set High ISO speed noise reduction to disable                EOS Manual P193

- set Long exp.noise reduction to off                                 EOS Manual P193

- set ISO between 100 and 400                                          EOS Manual P62

- preventing camera shake                                                  EOS Manual P106

- set Mirror lock up to Disable                                           EOS Manual P195

- set self-timer to 2 sec                                                       EOS Manual P70

- set White balance to Auto (AWB)                                   EOS Manual P99

- set image quality to RAW                                               EOS Manual P72

 

My camera has not been modified in any way e.g. by removing the internal infrared filter (not brave enough !!!).

 

2.2 DSLR colour channels

 

2.2.1 Bayer Matrix

 

A Bayer filter mosaic, Figure 2.1, is a color filter array for arranging RGB color filters on a square grid of photosensors, Figure 2.2. Its particular arrangement of color filters is used in most single-chip digital image sensors used in digital cameras, camcorders, and scanners to create a color image. The filter pattern is 50% green, 25% red and 25% blue, hence is also called RGBG, GRGB, or RGGB. It is named after its inventor, Bryce Bayer of Eastman Kodak. Each pixel only receives light filtered through one RGB colour. Software in the camera averages the other colours from surrounding pixels to calculate separate RGB values for each pixel.

 

As will be explained here the three channels can be separated and processed individually.

 

Bayer matrix

Figure 2.1. Bayer arrangement of colour filters

 

 

Bayer pattern

Figure 2.2. Cross-section of sensor

 

2.2.2 Spectral response

 

Figure 2.3 shows standard photometric filter response curves at the top and DSLR rgb filter response curves at the bottom. Wavelength of peak sensitivity of the DSLR g filter closely matches that of the Johnson V filter but has a narrower bandpass. DSLR r and b filter bandpasses are also narrower than the corresponding astronomical filters and their peak sensitivities are much closer together. So the overall DSLR spectral response is more compressed than standard BVR filters but DSLR photometry can be converted to Johnson-Cousins photometry as explained in Section 8.

 

Figure 2.3. Spectral responses of photometric filters and DSLR channels. Credit AAVSO DSLR Observing Manual/Mark Blandford

 

3.0 Imaging

 

3.1 Set-up

 

Figure 3.1 shows my imaging set-up including,

- Vixen Great Polaris GP-DX mount (originally purchased for a 10” Newtonian reflector)

- Vixen bar (to attach refractor ‘foot’ to mount)

- William Optics ZenithStar 71mm ED APO refractor

- WilliamOptics Flattener/Focal Reducer x0.8 for F6-A  APO

- Flat-6A Adapter (for Z71& Canon EOS)

- Canon EOS550D DSLR camera

- Red Dot finder (speaking from experience remember to attach this the right way round!!!)

 

In addition an external power supply was used for the camera to prevent battery going flat on long imaging runs.

 

IMG_4556

Fig 3.1. Imaging set-up

 

The Vixen bar was necessary as the telescope could not be balanced in declination with the camera attached due to the position of the refractor’s dovetail mount – my thanks to BAA member Simon Pinnock for suggesting this.

 

3.2 Linearity check

 

Using a light bin the pixel values for various exposure times and ISO settings were measured and plotted – Figure 3.2. As a result I use ISO400 and a saturation value of 11000 in Astrometrica settings – Figure 7.2. The maximum pixel value, 16304, for a 14 bit camera is shown on the chart.

 

Figure 3.2. Linearity check

 

3.3 Camera control

 

As described in Basic DSLR Astrophotography the camera is controlled from a laptop using the Canon EOS utility which is packaged with the camera - Backyard EOS is also popular.

 

3.4 Calibration frames

 

Dark and flat-dark frames were taken by covering the end of the telescope tube with a light-tight cap.  The exposure time for darks should be the same as for the images and for flat-darks the same time as for the flat fields. Best practice is to take at least five frames and combine them.

 

To obtain flat fields a light bin – Figure 3.3 – originally constructed for a 10”Newtonian reflector was used. To get the necessary 50% saturation level an exposure time of 15 secs was used – similarly for the Flat darks.

 

12

Figure 3.3. Light bin for flat fields

 

3.5 Focusing

 

Refractors bring objects to a focus in a curved plane. A field flattener will correct for this but objects will be offset the further they are from the centre of the image – Figure 3.4. Astrometrica settings must be such as to allow for this – Figure 20, Plate constants/4th-Order Fit is selected.

 

Figure 3.4. Astrometric offset

 

A Bahtinov mask was used to obtain a good focus. Centre and corners of image of a bright star were checked – Figure 3.5. When using a CCD camera on my 10” Newtonian reflector I had focused for the smallest ‘blob’ but this did not prove accurate enough for this set-up.

 

Bahtinov mask test

Figure 3.5. Enlarged portion of an image with Bahtinov mask in place

 

3.6 Images

 

On 2016 February 15th a series of images was obtained with exposure times of 1, 5, 10 and 20 secs respectively. Calibration frames were also obtained on the same night. The images were centred (more or less) on Capella so that this bright star could be used for accurate focusing.

 

4.0 Image processing

 

4.1 Process

 

Image processing is summarised in Figure 4.1.

 

If you wish to add FITS header data such as RA and Dec see Appendix 1 at the end of this document,

 

DSLR process

Figure 4.1. Process flow

 

4.2 AIP4WIN

 

(a) Convert RAW (CR2) cameras images to FITS

 

- set DSLR conversion settings/DeBayer, Convert Color to Greyscale, Red = Green = Blue = Gamma = 0.33333 – Figure 4.2.

 

Figure 4.2. AIP4WIN preferences

 

- open RAW (CR2) images and calibration frames and save as FITS

 

(b) Calibration set-up

 

- set up a Standard Calibration, median combining the dark, flat and flat dark frames using the previously saved FITS frames – Figures 4.3 and 4.4

 

Figure 4.3. Calibration set-up - Darks

 

Figure 4.4. Calibration set-up – Flats and Flat darks

 

(c) Calibrate FITS images

 

- open images and select Calibrate/Auto calibrate to calibrate images

- save calibrated image(s) as FITS

 

(d) Extract green channel (for V magnitudes)

 

- set DSLR conversion settings/DeBayer, Convert Color to Greyscale, Red=Blue=0. Green=Gamma=1 and Select De-Bayerization Algorithm/AHD – Figure 4.5

 

Figure 4.5. Green channel extraction settings

 

- load calibrated FITS image(s) and save after extracting green channel

- to avoid distortion, and therefore astrometry errors at the edges of the images, they were cropped form 2.5 x 3.5 degrees to 2.5 x 2.5 degrees using Transform/Crop

- rotate to north up, east left (my preferred orientation for Astrometrica) using Transform/Rotate 90 CW – Figure 4.6

 

Figure 4.6. Rotating and cropping image

 

Figure 4.7 is a Megastar chart of the approximate field of view of the image (before cropping). The bright star is Capella, Alpha Aurigae

 

Figure 4.7. Megastar chart of imaged star field

 

5.0 Photometry considerations

 

5.1  Magnitude range

 

The average magnitude error as computed by Astrometrica is 0.06 magnitudes and colour transformation (described later) appears to halve this. Further work remains to be done by imaging star fields of known accuracy e.g. Landolt, Hendon and BAA VSS fields.

 

The working magnitude range for a DSLR image is quite narrow – typically 3 magnitudes (Figure 5.3). The following explanation relates to a single 30 sec exposure time image.

 

To determine the faint limit a minimum SNR of 20 was chosen which would give an error of (1/SNR) +/-0.05. The minimum magnitude for various exposure times was obtained by measuring SNR vs magnitude using Astrometrica – see data below which suggests that the faint limit is magnitude 13.5.

 

OBSERVER:    R.Dymock

CONTACT:     Roger Dymock, 67 Haslar Crescent, Waterlooville, Hampshire, England, PO7 6D [roger.dymock@ntlworld.com]

TELESCOPE:   71 mm refractor plus DSLR

EXPOSURE JD: Mid-exposure, not corrected for light time

-----------------------------------------------------

      JD         mag        SNR    ZeroPt   Design.

-----------------------------------------------------

2457573.50000   10.154 V  239.74   22.327   A0001

2457573.50000   11.187 V  123.47   22.327   A0002

2457573.50000   12.043 V   68.50   22.327   A0003

2457573.50000   13.293 V   26.80   22.327   A0004

2457573.50000   13.776 V   14.83   22.327   A0005

----- end -----

 

To obtain the bright limit magnitudes were measured using Astrometrica and the max PV measured using the AIP4WIN star image tool. To keep the max PV below 11000 the brightest star should be magnitude 9.5 – Figures 5.1 and 5.2. As a confirmation the Upper Limit in Astrometrica, Figure 19, can be set to, say, 8.0. The errors, dV in Table 1, will then start to creep in for stars of magnitude 8.0 to 9.5.

 

Figure 5.1. Magnitude measurement using Astrometrica

 

Figure 5.2. Max Pixel Value for a magnitude 9.68 star using AIP4WIN

 

How to use the max and min values in Astrometrica is described in the extract from the Help file below.

Upper Limit: The upper limit for the magnitude of reference stars. If the field is rich in bright stars, the reference star match can fail because the brightest stars from the catalog (which are used to match the catalog to the image) are saturated in the image and are therefore not detected by the software. To avoid this problem, you can set the upper magnitude limit in Program Settings/Program to the magnitude where the stars in the CCD frame are saturated.

Lower Limit: The lower limit for the magnitude of reference stars. When the field is rich in stars, you might want to exclude the faint (potentially less precise) reference stars by specifying a lower limit. (Note that the settings in the Program Settings/Program/Residuals will automatically reject reference stars with large residuals.) You can also avoid reading large numbers of faint reference stars from the star catalog which are not detected in your images by specifying the approximate limiting magnitude of your images here.

5.2 Exposure times vs magnitude range

 

For a single 1 sec image range is 7.5 – 11.0 (min SNR = 20, error = +/- 0.05)

For a single 5 sec image range is 8.5 – 11.5 (“)

For a single 10 sec image range is 9.0 – 12.5  (“)

For a single 20 sec image range is 9.5 – 13.5 (“) (colour transform calculations suggest that 9.8 might be a better max mag limit)

For a stack of 5 x 10 sec (50 sec) images range is 11.0 – 13.5 (“)

For a stack of 5 x 20 sec (100 sec) images range is 11.5 – 14.5 (“)

 

Figure 5.3. Magnitude range

 

6.0 Astrometry considerations

 

The accuracy I am looking for here is < +/- 1 arcsec in both RA and Dec. A field flattener does not produce, for want of a better phrase, an astrometrically uniform image thus 4th-Order Fit rather than Linear Fit must be used in Program Settings/Program.

 

7.0 Astrometrica settings (for V magnitudes)

 

These are show in Figures 7.1 to 7.6

 

Figure 7.1. Program Settings/Observing site

 

Figure 7.2. Program Settings/CCD

 

Figure 7.3. Program Settings/Program. For crowded star fields use ‘Background from PSF’ otherwise use ‘Aperture’

 

Figure 7.4. Program Settings/Environment

 

Figure 7.5. Program Settings/Catalogs

 

Figure 7.6. Program Settings/Internet

 

8.0 Astrometry and Photometry using Astrometrica

 

8.1 Process

 

The process is quite simple – users of other astrometry and photometry software may be quite amazed as to how easy Astrometrica is to use and that it measures the position and magnitude of all stars (within the prescribed limits) in the image. So;

- open image in Astrometrica

- perform astrometry and photometry (centre of image is RA 05 16 45, Dec +46 18 43) – Figure 8.1 (the image was enlarged for better identification of stars)

 

Figure 8.1. Astrometrica screen shot showing astrometric and photometric results

 

At the lower right corner of the main screen, a popup-window gives a summary of the astrometric and photometric data. The number of stars (Detections),  the number of reference stars, the number of reference stars used for the astrometric data reduction, the mean residual (in arc seconds) for these reference stars, the number of reference stars used for photometry and their mean residual (in magnitudes).

 

8.2 Results and colour transformation

 

The process for obtaining Johnson-Cousins V, B and R magnitudes is shown in Figure 8.2 and described in the following paragraphs.

 

Figure 8.2. Process for obtaining Johnson-Cousins magnitudes from DSLR images

 

8.2.1 V magnitudes

 

The Astrometrica Log File was saved and imported into Excel – partial results are shown in Table 8.1 and all results plotted in Figure 8.4.

- V mag, and dV mag are output by Astrometrica

- UCAC4 V mag = V mag - dV mag

- dV mags were plotted against UCAC4 B-V magnitudes to obtain the colour transformation factor to convert Astrometrica V to Johnson-Cousins V - Figure 8.5

- the Transformation factor was applied to the Astrometrica V mags to produce Transformed V mags – Figure 8.6

- the average error was calculated for dV and dTV. It can be seen that the error is significantly reduced.

 

V

dV

UCAC4

UCAC

UCAC

Transform

Transformed

 

Abs

Abs

mag

mag

V mag

B mag

B-V

 

V mag

dTV

dV

dTV

11.98

0.16

11.82

13.48

1.66

0.13

11.85

0.03

0.16

0.03

12.05

0.1

11.95

13.15

1.20

0.08

11.97

0.02

0.10

0.02

11.87

-0.02

11.89

12.47

0.58

0.02

11.85

-0.04

0.02

0.04

11.56

0.14

11.42

12.66

1.24

0.09

11.47

0.05

0.14

0.05

11.68

-0.01

11.69

11.95

0.26

-0.02

11.70

0.01

0.01

0.01

11.64

0.03

11.61

12.24

0.63

0.02

11.62

0.01

0.03

0.01

11.54

0

11.54

12.03

0.49

0.01

11.53

-0.01

0.00

0.01

11.97

0.02

11.95

12.50

0.55

0.01

11.96

0.01

0.02

0.01

10.71

0

10.71

10.81

0.10

-0.03

10.74

0.03

0.00

0.03

10.56

0.18

10.38

11.80

1.42

0.11

10.45

0.07

0.18

0.07

11.25

0.09

11.16

12.31

1.15

0.08

11.17

0.01

0.09

0.01

10.28

0.1

10.18

11.31

1.13

0.08

10.20

0.02

0.10

0.02

10.92

0.09

10.83

11.84

1.01

0.06

10.86

0.03

0.09

0.03

9.84

-0.02

9.86

10.31

0.45

0.00

9.84

-0.02

0.02

0.02

11.06

0.04

11.02

11.47

0.45

0.00

11.06

0.04

0.04

0.04

11.75

0

11.75

12.31

0.56

0.01

11.74

-0.01

0.00

0.01

11.57

0.12

11.45

12.50

1.05

0.07

11.50

0.05

0.12

0.05

11.32

0.01

11.31

11.67

0.36

-0.01

11.33

0.02

0.01

0.02

10.93

0.01

10.92

11.16

0.24

-0.02

10.95

0.03

0.01

0.03

11.59

0.01

11.58

12.06

0.48

0.01

11.58

0.00

0.01

0.00

10.93

0

10.93

11.28

0.35

-0.01

10.94

0.01

0.00

0.01

11.66

-0.06

11.72

12.14

0.42

0.00

11.66

-0.06

0.06

0.06

12.09

-0.04

12.13

12.50

0.37

-0.01

12.10

-0.03

0.04

0.03

11.12

0.01

11.11

11.33

0.22

-0.02

11.14

0.03

0.01

0.03

10.23

0.09

10.14

11.31

1.17

0.08

10.15

0.01

0.09

0.01

11.29

0.07

11.22

11.76

0.54

0.01

11.28

0.06

0.07

0.06

11.02

0.14

10.88

12.17

1.29

0.09

10.93

0.05

0.14

0.05

12.1

-0.02

12.12

12.61

0.49

0.01

12.09

-0.03

0.02

0.03

12.1

0.18

11.92

13.97

2.05

0.17

11.93

0.01

0.18

0.01

11.93

-0.13

12.06

12.33

0.27

-0.02

11.95

-0.11

0.13

0.11

10.19

0.08

10.11

11.40

1.29

0.09

10.10

-0.01

0.08

0.01

12.10

0.08

12.02

13.54

1.52

0.12

11.98

-0.04

0.08

0.04

11.49

0.00

11.49

12.16

0.67

0.03

11.46

-0.03

0.00

0.03

11.04

0.09

10.95

12.31

1.36

0.10

10.94

-0.01

0.09

0.01

11.79

0.06

11.73

12.94

1.21

0.08

11.71

-0.02

0.06

0.02

10.71

0.03

10.68

11.00

0.32

-0.01

10.72

0.04

0.03

0.04

11.95

0.09

11.86

13.83

1.97

0.17

11.78

-0.08

0.09

0.08

10.61

-0.01

10.62

10.81

0.19

-0.03

10.64

0.02

0.01

0.02

11.31

-0.01

11.32

11.69

0.37

-0.01

11.32

0.00

0.01

0.00

11.85

0.04

11.81

12.43

0.62

0.02

11.83

0.02

0.04

0.02

11.78

0.03

11.75

12.34

0.59

0.02

11.76

0.01

0.03

0.01

11.17

-0.03

11.20

11.51

0.31

-0.01

11.18

-0.02

0.03

0.02

12.06

0.01

12.05

12.63

0.58

0.02

12.04

-0.01

0.01

0.01

10.81

-0.03

10.84

11.06

0.22

-0.02

10.83

-0.01

0.03

0.01

11.06

-0.01

11.07

11.61

0.54

0.01

11.05

-0.02

0.01

0.02

12.09

0.09

12.00

13.39

1.39

0.10

11.99

-0.01

0.09

0.01

11.81

0.01

11.80

12.29

0.49

0.01

11.80

0.00

0.01

0.00

11.99

0.00

11.99

13.24

1.25

0.09

11.90

-0.09

0.00

0.09

11.78

0.04

11.74

12.38

0.64

0.02

11.76

0.02

0.04

0.02

11.26

-0.04

11.30

11.75

0.45

0.00

11.26

-0.04

0.04

0.04

 

 

 

 

 

 

 

Average

0.05

0.03

Table 8.1. Photometric data.

 

UCAC4 B mags were obtained via Vizier at http://vizier.u-strasbg.fr/viz-bin/VizieR - Figure 8.3.

 

Figure 8.3. UCAC4 data from Vizier

 

A plot of Astrometrica vs UCAC4 V mags is shown in Figure 8.4

 

Figure 8.4 Astrometrica results

 

Figure 8.5. Colour transform plot

 

Figure 8.6. Transformed V mags

 

8.2.2 B magnitudes

 

The AIP4WIN and Astrometrica settings for extracting the blue channel and measuring the blue magnitudes are shown in Figures 8.7 and 8.8.

 

Figure 8.7. AIP4WIN Preferences/DSLR and Bayer Conversion Settings

 

Figure 8.8. Astrometrica Program Settings/CCD

 

The Astrometrica Log File was saved and imported into Excel – partial results are shown in Table 8.2 and all results plotted in Figure 8.9 

- B mag, and dB mag are output by Astrometrica

- UCAC4 B mag = B mag - dB mag

- dB mags were plotted against UCAC4 B-V magnitudes to obtain the colour transformation factor to convert Astrometrica B to Johnson-Cousins B - Figure 8.10

- the Transformation factor was applied to the Astrometrica B mags to produce Transformed B mags – Figure 8.11

- the average error was calculated for dB and dTB. It can be seen that the error is significantly reduced.

 

B

dB

UCAC

UCAC

UCAC

Transform

Transformed

 

Abs

Abs

mag

mag

V

B

B-V

 

B mag

dTB

dB

dTB

11.79

-0.62

11.01

12.41

1.40

-0.66

12.45

0.04

0.62

0.04

12.67

-0.47

11.95

13.14

1.19

-0.48

13.15

0.01

0.47

0.01

12.65

0.18

11.89

12.47

0.58

0.03

12.62

0.15

0.18

0.15

11.76

0.37

11.23

11.39

0.16

0.38

11.38

-0.01

0.37

0.01

11.93

0.26

11.40

11.67

0.27

0.29

11.64

-0.03

0.26

0.03

12.20

-0.46

11.43

12.66

1.23

-0.52

12.72

0.06

0.46

0.06

12.27

0.32

11.69

11.95

0.26

0.30

11.97

0.02

0.32

0.02

12.19

-0.05

11.61

12.24

0.63

-0.01

12.20

-0.04

0.05

0.04

12.15

0.12

11.54

12.03

0.49

0.11

12.04

0.01

0.12

0.01

11.28

0.47

10.71

10.81

0.10

0.43

10.85

0.04

0.47

0.04

11.17

-0.63

10.38

11.80

1.42

-0.67

11.84

0.04

0.63

0.04

11.82

-0.49

11.16

12.31

1.15

-0.45

12.27

-0.04

0.49

0.04

10.91

-0.40

10.18

11.31

1.13

-0.43

11.34

0.03

0.4

0.03

9.86

-0.06

9.52

9.92

0.40

0.18

9.68

-0.24

0.06

0.24

11.49

-0.36

10.83

11.85

1.02

-0.34

11.83

-0.02

0.36

0.02

10.39

0.08

9.86

10.31

0.45

0.14

10.25

-0.06

0.08

0.06

11.66

0.19

11.02

11.47

0.45

0.14

11.52

0.05

0.19

0.05

12.41

0.09

11.75

12.32

0.57

0.04

12.37

0.05

0.09

0.05

12.13

-0.37

11.45

12.50

1.05

-0.36

12.49

-0.01

0.37

0.01

11.88

0.21

11.31

11.67

0.36

0.22

11.66

-0.01

0.21

0.01

11.52

0.36

10.92

11.16

0.24

0.31

11.21

0.05

0.36

0.05

12.17

0.11

11.58

12.06

0.49

0.11

12.06

0.00

0.11

0.00

11.51

0.23

10.92

11.28

0.36

0.22

11.29

0.01

0.23

0.01

12.75

0.25

12.13

12.5

0.37

0.21

12.54

0.04

0.25

0.04

11.70

0.37

11.12

11.33

0.21

0.34

11.36

0.03

0.37

0.03

10.84

-0.47

10.14

11.31

1.17

-0.46

11.30

-0.01

0.47

0.01

11.84

0.08

11.21

11.76

0.55

0.06

11.78

0.02

0.08

0.02

11.61

-0.56

10.88

12.17

1.29

-0.56

12.17

0.00

0.56

0.00

10.76

-0.64

10.11

11.40

1.29

-0.57

11.33

-0.07

0.64

0.07

10.20

-0.32

9.46

10.52

1.06

-0.37

10.57

0.05

0.32

0.05

12.64

0.18

12.03

12.46

0.43

0.16

12.48

0.02

0.18

0.02

11.65

-0.67

10.94

12.32

1.38

-0.64

12.29

-0.03

0.67

0.03

12.40

-0.54

11.73

12.94

1.21

-0.50

12.90

-0.04

0.54

0.04

11.30

0.29

10.68

11.01

0.33

0.24

11.06

0.05

0.29

0.05

11.20

0.4

10.62

10.80

0.18

0.37

10.83

0.03

0.40

0.03

12.43

0

11.81

12.43

0.62

0.00

12.43

0.00

0.00

0.00

11.75

0.25

11.20

11.50

0.30

0.27

11.48

-0.02

0.25

0.02

12.73

0.1

12.05

12.63

0.58

0.03

12.70

0.07

0.10

0.07

10.34

-0.11

9.86

10.45

0.59

0.02

10.32

-0.13

0.11

0.13

11.33

0.27

10.84

11.06

0.23

0.33

11.00

-0.06

0.27

0.06

11.03

0.11

10.46

10.92

0.46

0.13

10.90

-0.02

0.11

0.02

11.69

0.08

11.08

11.61

0.53

0.07

11.62

0.01

0.08

0.01

12.65

-0.74

12.00

13.39

1.39

-0.65

13.30

-0.09

0.74

0.09

12.46

0.17

11.80

12.29

0.49

0.11

12.35

0.06

0.17

0.06

12.81

-0.43

11.99

13.24

1.25

-0.53

13.34

0.10

0.43

0.10

12.45

0.08

11.74

12.37

0.63

-0.01

12.46

0.09

0.08

0.09

11.83

0.08

11.30

11.75

0.45

0.14

11.69

-0.06

0.08

0.06

12.77

0.08

12.33

12.69

0.36

0.21

12.56

-0.13

0.08

0.13

12.70

-0.25

12.02

12.95

0.93

-0.26

12.96

0.01

0.25

0.01

11.76

-0.57

11.07

12.33

1.26

-0.54

12.30

-0.03

0.57

0.03

 

 

 

 

 

 

 

Average

0.30

0.05

Table 8.2. Photometric data

 

Figure 8.9. Astrometrica results

 

 

Figure 8.10. Colour transform plot

 

Figure 8.11. Transformed B mags

 

8.2.3 R magnitudes

 

The UCAC4 catalogue includes Sloan r’ rather than Johnson-Cousins R magnitudes but the latest version of Astrometrica, 4.10.0.421 translates these to the aforementioned R magnitudes using a formula I devised, Rc = r’ – 0.108 x (B – V)-0.1322 to convert r’ to Rc. Please note this formula has yet to be formally proven but it seems to work !!! An explanation as to how the formula was calculated is given in 8.2.4.1 below.

 

The AIP4WIN and Astrometrica settings for extracting the red channel and measuring the red magnitudes are shown in Figures 8.12 and 8.13.

 

Figure 8.12. AIP4WIN Preferences/DSLR and Bayer Conversion Settings

 

Figure 8.13. Astrometrica Program Settings/CCD

 

The Astrometrica Log File was saved and imported into Excel – partial results are shown in Table 8.3 and plotted in Figure 8.14

- Ra mag, and dRa mags are output by Astrometrica

- Bu, Vu, r’u are from the UCAC4

- calc Ru is calculated from the equation above

- dRa mags were plotted against UCAC4 B-V magnitudes to obtain the colour transformation factor to produce convert Astrometrica R to Johnson-Cousins Rc

  Figure 8.15

- the Transformation factor was applied to the Astrometrica Ra mags to produce Transformed Ra mags (Equivalent to Johnson-Cousins R) – Figure 8.16

- the average error was calculated for Transformed Ra-calc Ru. It can be seen that the error is reduced by approximately 2/3rd.

 

Table 8.3. Photometric data

 

(New PC and Excel 2016 hence change in chart layout)

 

Figure 8.14. Astrometrica results

 

Figure 8.15. Colour transform plot

 

Figure 8.16. Transformed Astrometrica R magnitudes

 

8.2.4 Landolt standard fields

 

8.2.4.1 Derivation of equation Rc = r’–0.108 x (B–V)-0.1322

 

UCAC4 red magnitude is r’ rather than Rc but r’ mags can be transformed to Rc mags using the equation Rc = (r'-0.19xV-0.13)/0.81 which is a rearrangement of r' = V-0.81(V-Rc)+0.13 from the paper 'The u'g'r'I'z' Standard Star System’ by Allyn-Smith et al. Astron. J. 123, 2122-2144 (2002), Table 7, which can be found at http://iopscience.iop.org/article/10.1086/339311/pdf or by my equation Rc = r’–0.108 x (B–V)-0.1322.

 

Table 8.4 lists data for a sample of 50 Landolt stars plus the relevant data from the UCAC4 catalogue.

 

Landolt

 

UCAC4

 

 

 

 

RA

Dec

V

B-V

V-R

B

Rc

B

V

r'

R-r'

B-V

Transform

Rt=r'-0.108(B-V)-0.1322

Rc-Rt

Abs(R-Rt)

00:54:16

+00:39:51

13.818

1.418

0.929

15.236

12.889

15.271

13.815

13.212

-0.323

1.456

-0.289

12.923

-0.034

0.034

00:54:34

+00:41:05

14.325

0.699

0.399

15.024

13.926

15.060

14.318

14.118

-0.192

0.742

-0.212

13.906

0.020

0.020

00:54:37

+00:38:56

13.178

0.814

0.446

13.992

12.732

14.017

13.176

12.934

-0.202

0.841

-0.223

12.711

0.021

0.021

00:54:48

+00:39:23

14.932

0.517

0.326

15.449

14.606

15.483

14.939

14.802

-0.196

0.544

-0.191

14.611

-0.005

0.005

00:54:52

+00:40:20

14.085

1.131

0.719

15.216

13.366

15.268

14.081

13.606

-0.240

1.187

-0.260

13.346

0.020

0.020

00:55:15

+01:01:49

14.984

0.398

0.239

15.382

14.745

15.619

15.003

14.904

-0.159

0.616

-0.199

14.705

0.040

0.040

00:55:16

+01:01:53

15.036

0.457

0.285

15.493

14.751

15.619

15.003

14.904

-0.153

0.616

-0.199

14.705

0.046

0.046

00:55:10

+00:43:14

11.613

0.436

0.266

12.049

11.347

12.069

11.604

11.516

-0.169

0.465

-0.182

11.334

0.013

0.013

00:55:40

+00:36:18

11.782

1.048

0.563

12.830

11.219

12.835

11.772

11.443

-0.224

1.063

-0.247

11.196

0.023

0.023

00:55:59

+00:52:58

13.941

1.191

0.755

15.132

13.186

15.188

13.942

13.436

-0.250

1.246

-0.267

13.169

0.017

0.017

00:56:06

+00:50:47

14.965

1.164

0.759

16.129

14.206

16.196

14.970

14.475

-0.269

1.226

-0.265

14.210

-0.004

0.004

00:56:16

+00:53:16

14.44

0.567

0.338

15.007

14.102

15.072

14.413

14.283

-0.181

0.659

-0.203

14.080

0.022

0.022

00:56:27

+00:41:53

12.036

0.629

0.368

12.665

11.668

12.690

12.028

11.860

-0.192

0.662

-0.204

11.656

0.012

0.012

00:56:47

+00:38:29

12.969

0.318

0.201

13.287

12.768

13.320

12.960

12.929

-0.161

0.360

-0.171

12.758

0.010

0.010

00:57:17

+00:36:46

11.63

0.855

0.489

12.485

11.141

12.495

11.620

11.341

-0.200

0.875

-0.227

11.114

0.027

0.027

02:30:17

+05:15:51

12.799

-0.054

-0.103

12.745

12.902

12.740

12.802

13.026

-0.124

-0.062

-0.126

12.900

0.002

0.002

02:35:08

+03:43:57

12.411

-0.203

0.09

12.208

12.321

12.258

12.442

12.522

-0.201

-0.184

-0.112

12.410

-0.089

0.089

02:53:38

+00:17:19

12.659

0.817

0.48

13.476

12.179

13.466

12.660

12.401

-0.222

0.806

-0.219

12.182

-0.003

0.003

02:57:21

+00:18:38

11.728

0.301

0.178

12.029

11.550

12.035

11.723

11.713

-0.163

0.312

-0.166

11.547

0.003

0.003

02:57:46

+00:16:02

11.204

1.219

0.659

12.423

10.545

12.426

11.202

10.793

-0.248

1.224

-0.264

10.529

0.016

0.016

02:58:13

+01:10:53

11.594

1.418

0.756

13.012

10.838

13.008

11.590

11.095

-0.257

1.418

-0.285

10.810

0.028

0.028

05:57:37

+00:13:44

9.780

0.199

0.120

9.979

9.660

9.984

9.769

9.758

-0.098

0.215

-0.155

9.603

0.057

0.057

05:58:25

+00:05:14

10.790

1.359

0.771

12.149

10.019

12.145

10.771

10.280

-0.261

1.374

-0.281

9.999

0.020

0.020

05:57:55

-00:09:28

11.480

1.870

1.051

13.350

10.429

13.322

11.482

10.775

-0.346

1.840

-0.331

10.444

-0.015

0.015

05:57:33

+00:21:16

11.610

1.659

0.931

13.269

10.679

13.272

11.608

10.999

-0.320

1.664

-0.312

10.687

-0.008

0.008

05:57:07

+00:01:12

11.730

0.650

0.370

12.380

11.360

12.399

11.728

11.563

-0.203

0.671

-0.205

11.358

0.002

0.002

05:58:09

+00:19:00

12.970

0.810

0.520

13.780

12.450

13.762

12.953

12.682

-0.232

0.809

-0.220

12.462

-0.012

0.012

05:58:07

+00:12:19

14.710

1.940

1.080

16.650

13.630

16.797

14.747

14.010

-0.380

2.050

-0.354

13.656

-0.026

0.026

05:57:46

+00:12:43

14.820

1.099

0.700

15.919

14.120

15.936

14.863

14.450

-0.330

1.073

-0.248

14.202

-0.082

0.082

06:51:34

-00:11:28

10.572

0.609

0.349

11.181

10.223

11.182

10.552

10.409

-0.186

0.630

-0.200

10.209

0.014

0.014

06:51:50

-00:21:17

12.723

2.192

1.254

14.915

11.469

14.959

12.703

11.828

-0.359

2.256

-0.376

11.452

0.017

0.017

06:52:02

-00:27:21

10.536

0.202

0.109

10.738

10.427

10.722

10.539

10.594

-0.167

0.183

-0.152

10.442

-0.015

0.015

06:52:04

-00:27:18

10.030

1.180

0.615

11.210

9.415

11.173

10.039

9.660

-0.245

1.134

-0.255

9.405

0.010

0.010

06:52:10

-00:23:34

12.732

0.164

0.091

12.896

12.641

12.889

12.736

12.800

-0.159

0.153

-0.149

12.651

-0.010

0.010

06:52:19

-00:23:34

12.754

0.293

0.158

13.047

12.596

13.064

12.757

12.766

-0.170

0.307

-0.165

12.601

-0.005

0.005

06:52:05

-00:18:19

9.539

-0.004

0.009

9.535

9.530

9.532

9.526

9.653

-0.123

0.006

-0.133

9.520

0.010

0.010

06:52:05

-00:19:40

12.271

0.157

0.080

12.428

12.191

12.416

12.324

12.349

-0.158

0.092

-0.142

12.207

-0.016

0.016

06:52:12

-00:18:22

13.385

0.968

0.575

14.353

12.810

14.394

13.347

13.011

-0.201

1.047

-0.245

12.766

0.044

0.044

06:52:12

-00:19:17

11.930

1.356

0.723

13.286

11.207

13.287

11.953

11.488

-0.281

1.334

-0.276

11.212

-0.005

0.005

06:52:14

-00:19:21

13.068

1.146

0.683

14.214

12.385

14.277

13.090

12.671

-0.286

1.187

-0.260

12.411

-0.026

0.026

06:52:14

-00:19:41

13.398

1.909

1.082

15.307

12.316

15.324

13.410

12.697

-0.381

1.914

-0.339

12.358

-0.042

0.042

06:52:17

-00:19:42

13.749

0.632

0.366

14.381

13.383

14.422

13.769

13.610

-0.227

0.653

-0.203

13.407

-0.024

0.024

06:52:19

-00:20:19

11.954

0.463

0.290

12.417

11.664

12.442

11.944

11.842

-0.178

0.498

-0.186

11.656

0.008

0.008

06:52:21

-00:15:50

14.439

1.595

0.928

16.034

13.511

16.185

14.475

13.849

-0.338

1.710

-0.317

13.532

-0.021

0.021

06:52:28

-00:13:43

12.113

0.314

0.193

12.427

11.920

12.419

12.106

12.090

-0.170

0.313

-0.166

11.924

-0.004

0.004

06:52:38

-00:16:34

13.707

0.315

0.173

14.022

13.534

14.052

13.735

13.730

-0.196

0.317

-0.166

13.564

-0.030

0.030

06:52:38

-00:17:05

14.090

0.595

0.376

14.685

13.714

14.754

14.146

13.953

-0.239

0.608

-0.198

13.755

-0.041

0.041

06:52:38

-00:19:22

11.118

1.104

0.575

12.222

10.543

12.199

11.112

10.774

-0.231

1.087

-0.250

10.524

0.019

0.019

06:52:40

-00:17:16

12.238

1.285

0.698

13.523

11.540

13.513

12.237

11.806

-0.266

1.276

-0.270

11.536

0.004

0.004

10:00:47

-07:33:31

13.561

-0.215

-0.098

13.346

13.659

13.392

13.562

13.782

-0.123

-0.170

-0.114

13.668

-0.009

0.009

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Average

0.021

Table 8.4. Landolt and UCAC4 data

 

To obtain the colour transformation (R-r’) was plotted against UCAC4 (B-V) – Figure 8.17. The slope of the graph gives the transform coefficient, (R-r’)=-0.108(B-V)-0.1322, and therefore R=r’-0.108(B-V)-0.1322

 

Figure 8.17. Transform

 

The transformed magnitudes were then plotted against Landolt R magnitudes – Figure 8.18. It can be seen that the transformed magnitudes are a very good fit with Landolt magnitudes - the average error being 0.21

 

Figure 8.18. Transformed magnitudes

 

8.2.4.2 Comparison of two equations mentioned in 8.2.4.1

 

Rc was calculated using both equations for a sample of Landolt stars  - the data are shown in Table 8.5 and Rc vs Landolt R plotted in Figure 8.19. The average errors for both equations are very similar at 0.017 and 0.019 respectively.  Rcr uses my equation and Rcas that devised by Allyn-Smith et al.

 

Landolt

UCAC4

 

 

 

 

RA

Dec

V

B-V

V-R

B

R

B

V

r'

Rcr

Rcas

R-Rcr

R-Rcas

 

 

 

 

 

 

 

 

 

 

 

 

 

 

00:54:16

+00:39:51

13.818

1.418

0.929

15.236

12.889

15.271

13.815

13.212

12.923

12.910

-0.034

-0.021

00:54:34

+00:41:05

14.325

0.699

0.399

15.024

13.926

15.060

14.318

14.118

13.906

13.911

0.020

0.015

00:54:37

+00:38:56

13.178

0.814

0.446

13.992

12.732

14.017

13.176

12.934

12.711

12.717

0.021

0.015

00:54:48

+00:39:23

14.932

0.517

0.326

15.449

14.606

15.483

14.939

14.802

14.611

14.609

-0.005

-0.003

00:54:52

+00:40:20

14.085

1.131

0.719

15.216

13.366

15.268

14.081

13.606

13.346

13.334

0.020

0.032

00:55:15

+01:01:49

14.984

0.398

0.239

15.382

14.745

15.525

14.932

14.870

14.674

14.695

0.071

0.050

00:55:16

+01:01:53

15.036

0.457

0.285

15.493

14.751

15.525

14.932

14.870

14.674

14.695

0.077

0.056

00:55:10

+00:43:14

11.613

0.436

0.266

12.049

11.347

12.069

11.604

11.516

11.334

11.335

0.013

0.012

00:55:40

+00:36:18

11.782

1.048

0.563

12.830

11.219

12.835

11.772

11.443

11.196

11.205

0.023

0.014

00:55:59

+00:52:58

13.941

1.191

0.755

15.132

13.186

15.188

13.942

13.436

13.169

13.157

0.017

0.029

00:56:06

+00:50:47

14.965

1.164

0.759

16.129

14.206

16.196

14.970

14.475

14.210

14.198

-0.004

0.008

00:56:16

+00:53:16

14.440

0.567

0.338

15.007

14.102

15.072

14.413

14.283

14.080

14.092

0.022

0.010

00:56:27

+00:41:53

12.036

0.629

0.368

12.665

11.668

12.690

12.028

11.860

11.656

11.660

0.012

0.008

00:56:47

+00:38:29

12.969

0.318

0.201

13.287

12.768

13.320

12.960

12.929

12.758

12.761

0.010

0.007

00:57:17

+00:36:46

11.630

0.855

0.489

12.485

11.141

12.495

11.620

11.341

11.114

11.115

0.027

0.026

 

 

 

 

 

 

 

 

 

 

 

 

0.019

0.017

Table 8.5. Photometric data

 

Figure 8.19. Transformed magnitudes

 

8.3 Three colour photometry

 

The R, G, B magnitudes of several stars were obtained using Astrometrica and plotted in Figure 8.20. The positions of the curves have been adjusted to better show how the colour bands relate to the different types of stars. It could have been done using the catalogue values but you won’t necessarily have all these for a comet or asteroid. As you would expect as the stars get hotter B brightens relative to R – very few stars in my image (approx 1%) have B brighter than R but this may be a selection effect of the magnitude range used.

 

Figure 8.20. Three colour photometry

 

Ballesteros’ formula for calculating star temperature, T, from the B-V index is;

 

T = 4600((1/0.92(B-V)+1.7)+1/(0.92(B-V)+0.62))

 

8.4 Further work

 

Photometric accuracy

 

Work remains to be done to verify photometry accuracy. This will include imaging stars whose accuracy is well defined e.g;

- Landolt Standard Fields.  These can be found in ‘A Practical Guide to Lightcurve Photometry and Analysis’ or downloaded from http://james.as.arizona.edu/~psmith/atlasinfo.html

- VSS fields (http://www.britastro.org/vss/)

 

Astrometry and BVR photometry of asteroids and comets

 

Two for one !!!. Asteroid-asteroid appulses are listed at http://www.minorplanet.info/ObsGuides/Appulses/AsteroidAppulses.htm

 

Asteroid (3 colour ?) lightcurves

 

Lists of observable comets can be found at; http://www.ast.cam.ac.uk/~jds/ and http://aerith.net/comet/weekly/current.html

 

Colour transformation applied to asteroids and comets;

 

Trawling through my book and various websites I found B-V values of 0.7 for C types and 0.9 for S types.

 

For comets I found the following at http://webdelprofesor.ula.ve/ciencias/ferrin/tablas/tablavri2.txt

0.46 < B-V < 1.08, average B-V = 0.76±0.16. This webpage does list B-V values for a number of comets but, if not known, I guess I could use the average value which would mean a similar correction to that for asteroids. 
 
The same website lists V-R values for comets – typically 0.5 or so. Asteroids also have similar values, 0.4 to 0.5 – from http://www.minorplanet.info/MPB/MPB_35-3.pdf

 

Acknowledgements

 

My thanks to the following for their help with this project

Richard Berry

Luca Buzzi

Tim Crawford

Martin Crow

Nick Evetts

Nick James

Des Loughney

Roger Pickard

 

And especially Richard Miles and Herbert Raab

 

References

 

DSLR Photometry by Mike Durkin - http://www.britastro.org/vss/DSLR_PHOTOMETRY.pdf

Variable star photometry with a DSLR camera by Des Loughney - http://www.britastro.org/vss/JBAA%20120-3%20%20Loughney.pdf

AAVSO DSLR Observing Manual - https://www.aavso.org/dslr-observing-manual

AAVSO DSLR Photometry Tutorial - https://www.aavso.org/dslr-photometry-tutorial-0

 

Appendix 1

 

Astroart allows you to edit the FITS header to add such data as RA and Dec which is useful when performing astrometry and photometry with Astrometrica as you do not then have to enter the coordinates manually. To do so;

- open the image in Astroart and select Edit/Header FITS

- place the cursor at the end of a line and press return

- enter the RA and Dec coordinates as shown in Figure A1.1

- close the text edit window

- File/Save FITS (or use the Save icon). The image is saved as .fit rather than .fts

 

Figure A1.1. Editing the FITS header

 

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