Herramientas Informáticas 53

4.2.1

Field of View

The “angle of view” describes the angular extent of a given scene that is imaged by a camera. It is used interchangeably with the more general term field of view (FOV) and for lenses projecting non-spatially-distorted images of distant objects, the effective focal length and the image format dimensions completely define the FOV. The manufacturer of the Mamiya 654 lens used by the KELT-South telescope lists the angle of view at 47◦. However, when used in combination with the CCD sensor, the total FOV of the telescope can be calculated as follows:

α = 2arctan d

2f (4.1)

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where d is the detector size (in either the horizontal or vertical direction) and f is the focal length of the lens. In KELT-South the detector is 36.88×36.88 mm in size and the focal length of the lens is listed as 80 mm. This results in a viewable area for the KELT-South telescope of 25.96◦×25.96◦.

4.2.2

Plate Scale

Figure 4.1: Image of known star field showing the stars used to determine the plate scale of the telescope.

The plate scale of the telescope was determined in three different ways. The first method simply uses the FOV of the telescope and the number of pixels on the CCD detector. For KELT-South the FOV is 25.96◦ and the number of pixels is 4096. The plate scale was determined to be 22.8200pixel−1.

The second method to determine the plate scale involved the following steps: • Take an image of a known part of the sky.

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4.2 Telescope Field of View and Plate Scale 93

Table 4.1: Table of the positions of stars used to determine plate scale. Only the first 10 entries are listed, but all 50 were used to calculate the plate scale.

USNO-B1 Name X Pos Y Pos RA (J2000) Dec (J2000)

0890-0058128 41.06 545.95 80.942745 -0.945584 0875-0097020 77.11 303.87 81.168242 -2.497848 0871-0085948 91.01 254.08 81.255006 -2.81547 0911-0059958 90.07 878.64 81.26465 1.185595 0894-0059248 108.99 608.67 81.379495 -0.543953 0879-0095426 117.96 375.16 81.429912 -2.040312 0857-0058873 168.07 23.01 81.743814 -4.299139 0889-0059897 171.97 524.94 81.780548 -1.083075 0900-0061288 222.08 696.96 82.107295 0.020334 0912-0061718 232.06 885.07 82.175384 1.22697

• Identify a number of non-saturated stars in the image using the IMSTAR utility (central pixel location for saturated stars is poorly defined).

• Determine the pixel coordinate location of each star.

• Determine the distance in pixels from every star to each of the others and record those values.

• Compare the list of identified stars with an online catalogue to find the celestial coor- dinates of each one.

• Determine the angular distance from every star to each of the others and record the values.

• Determine the plate scale by dividing the angular distance by the pixel distance. • Calculate the mean and standard deviation of all the plate scales determined. Figure 4.1 shows the locations of the stars used to determine the plate scale and Table 4.1 lists the relevant information for all the stars. The pixel separation can be determined by the Pythagoras theorem:

D =p(x2− x1)2+ (y2− y1)2 (4.2)

where D is the pixel distance between the two stars on the image, x1 and x2 are the X

coordinates of the two stars and y1and y2 are the Y coordinates of the two stars. Angular

separation was determined as follows:

θ = tan−1 

 q

cos2_δ

2sin2(α2− α1) + [cos δ1sin δ2− sin δ1cos δ2cos(α2− α1)]2

sin δ1sin δ2+ cos δ1cos δ2cos(α2− α1)



 (4.3)

where θ is the angular distance between two of the stars, α1, α2, δ1 and δ2 are the right

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1225 pairs of stars were determined and the plate scale was determined for each of these pairs. Finally the mean plate scale was determined. Using this method the plate scale was determined to be 23.09±0.0100 pixel−1.

A third method to determine the plate scale was to upload the image to the Astrom- etry.net website and obtain a coordinate solution for the image shown in Figure 4.1. Astrometry.net is capable of providing coordinate solutions using blind search meth- ods and in the process provides an estimate for the plate scale of the image (see Section 5.2.4 for a detailed description of how this program works). The plate scale estimate from Astrometry.net was 23.1100 pixel−1.

0

500

1000

1500

2000

2500

3000

Distance from centre of CCD chip [pixels]

21.8

22.0

22.2

22.4

22.6

22.8

23.0

23.2

23.4

Pixel Scale [arcsec pixel

−

1

]

Figure 4.2: Plot of the plate scale as a function of the radial distance from the centre of the CCD chip.

The three values determined above can be seen as a “special” average plate scale. In reality, the plate scale of the telescope will vary with radial distance from the centre of the CCD chip due to the barrel distortion introduced by the wide field of view of the Mamiya lens. To show how the plate scale changes across the FOV, the eastern orientation Target1 reference image (see Section 5.2 for more details) was cut into 400 blocks of 256×256 pixels in size, arranged in a 20×20 grid equally spaced across the entire image (some of the blocks overlap slightly). Each of these blocks was then analysed with Astrometry.net and the plate scale of each block as well as the central pixel coordinate of each block recorded. Figure 4.2 shows how the plate scale changes as a function of radial distance from the centre of the

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