You, too, can make useful and beautiful astronomical images at Mees: Lesson 1

Useful references: The Mees telescope startup/shutdown guide:

http://www.pas.rochester.edu/~dmw/ast142/Projects/Chklist.pdf

The AST 142 Projects manual:http://www.pas.rochester.edu/~dmw/ast142/Projects/Project.pdf

AST 203 lectures 19 and 24:http://www.pas.rochester.edu/~dmw/ast203/

Rob Gendler (ed.) 2013, Lessons from the Masters (New York: Springer-Verlag), especially the articles by Adam Block (p. 159) and Stan Moore (p. 1).

Software:

TheSky, or Stellarium (http://www.stellarium.org).

CCDSoft v. 5.16 June 2016 CCD imaging lessons 1

Some recent Mees results to whet your enthusiasm. You all know the Big Dipper:

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Van Gogh 1888

The Big DipperTop ten galaxiesnear the Big Dipper

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M101

M51

M63

M94M106

M109M108

M82

M81

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M109

LRGB, 4.0 hours total

24 May 2016, DMW

13.1’x11.3’

N

E

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M51

LRGB, 4 hours total

10 June 2016, DMW

13.9’x12.0’

N

E

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M101

LRGB, 4.5 hours total

15 June 2016, DMW

15.4’x13.1’

N

E

The short answer: a recipe to make such images

Identify a date range and a favorite object which is high in the sky at night for at least 3-4 hours on those dates.

Compile or plan to take the calibration data.

• Dark and bias frames are compiled for you on the CCD-camera computer, as long as you use the CCD camera at either T = -10 C or -20 C.

• Flat field frames are provided too but it’s a good idea to take new ones: 32-64 frame sequences in each filter, pointed at clear sky near zenith, starting at sunset.

• For scientifically useful data: identify some 8-10 mag A stars near your target.

Plan to autoguide on all deep-sky targets; identify a nearby 6-12 mag star about 12 arcminutes east of your target.

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Recipe (continued)

For scientifically useful images:

• Equal numbers of frames in R, G, B, interspersed occasionally with short R, G, B frames on calibration stars, all binned 2x2 pixels.

• As many frames as you have time for.

• 5 minute exposures in moonlight; 8-10 minute exposures in dark skies. All will be averaged together in the end.

For pretty pictures: as above but

• 3-4 times as many L frames as any of R, G, B, in 1x1 binning.

• Again, as many frames as you have time for in > 4 hours.

• No need to do the standard stars.

• Note that most APOD images involve >> 4 hours.

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Recipe (continued)

These Lessons, of which today is just the first, are intended to teach you

the details of following the recipe: how to use the camera SW, how to autoguide, etc.

the simple physics behind imaging observations.

the tricks of data reduction useful in scientifically useful imaging (e.g. IDL, CCDStack, MEM deconvolution) …

and those useful in making pretty pictures: the above, plus FITS Liberator and Adobe Photoshop.

All software to be discussed in all lessons is installed on the two Intro Astronomy Lab laptop computers; some is also site licensed; other useful programs can be had for Free.

Now for some of the technical details…

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Sensitivity and signal-to-noise ratio

“Sensitive” means large ratio of signal and noise.Signal = photocurrent from celestial objects. For small bandwidths – that is, filter width

At visible wavelengths and with CCDs, one can take emissivity ε to be zero and photoconductive gain g to be 1. The other terms are

τ Transmission of optics; range = 0-1η Quantum efficiency of detector; range = 0-1λ Wavelength; range = 300-700 nm for visible lighth, c, qe physical constants, by their usual symbols

( )1 SS e

PI gqhcλ

ε τη= −

,λ λ∆

Sensitivity and signal-to-noise ratio (continued)

Because of the finite, quantized electron charge, and random arrival time of electrons at given points in a circuit, there is noise in photocurrent. Shorthand for this effect: shot noise.

Here, we refer to a single pixel or group of pixels in the CCD, and

PS power from target, incident on pixelPB incident background power (e.g. moonlight, city lights)ID dark current: current drawn by pixel even when no light shines∆t exposure time: time over which current is averaged16 June 2016 CCD imaging lessons 11

( ) ( )

( )

2 2 e eN S B D

e eS B D

q I qI I I I I

t tq q

P P It hcλτη

= ∆ = = + +∆ ∆

= + + ∆

Sensitivity and signal-to-noise ratio (continued)

So the signal-to-noise ratio is

Usually one of the terms in the denominator dominates the others: Background-limited:

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( )

( )

1 2

2 2

e eS Se S B D

N

S

S B De

q qI PS q P P IN I hc t hc

P th chc P P I

q

λτηλτη

λτη

λτη

− ≡ = + + ∆

= ∆+ +

S SBL B

S P t P tN hcP

λτη η = ∆ ∝ ∆

B S D eP P ,hcI q .λτη

Sensitivity and signal-to-noise ratio (continued)

Source limited:

Dark-current limited:

Note that in all cases S/N increases with . To increase S/N by a factor of two, one needs to increase the exposure time by a factor of 4.

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SS

BL

PS t P tN hc

λτηη = ∆ ∝ ∆

S B D eP P ,hcI q .λτη

D B SI P hc , P hc .λτη λτη

eSS

DL D

qPS t P tN hc I

λτηη = ∆ ∝ ∆

t∆

Our system

Mees 24-inch Cassegrain telescope.

f/13.5, 25 arcsec per mm in Cassegrain focal plane.

Unvignetted field of view 24 arcmin in diameter.

Collecting area 2700 cm2.

Santa Barbara Instrument Group (SBIG) STX 16803 CCD camera.

Frame-transfer CCD, 4096x4096, 9 µm pixels (0.224 arcsec/pixel, 15.4 arcmin on a side, 21.7 arcmin diagonal), plus separate interline autoguiding CCD, 657x495, 7.4 µm pixels.

η = 0.5-0.6 across the visible band. 16-bit output; 1.27 electrons per data number (DN).

ID = 0.009 electrons per sec at T = -20 C.

9-electron read noise.

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Our system (continued)

Baader Planetarium filters: L, R, G, B, Hα; peak

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0 98. .τ ≅

Objects in the sky, or on TheSky

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Secret astronomer unit: the magnitude.

All you need to know is that, for two objects A and B, their fluxes (power per unit area, in real physics units) and magnitudes are related by

Past that, one just needs the conversion to/from physical units for a zero-magnitude star (Vega). Here, for the Johnson filters:

( )2 5logA B B Am m . F F− =

Examples

1. What is the power that the Mees telescope collects from a 10th magnitude A0V star, within the bandwidth of the G filter?

From the spectrum above we see that the G filter covers wavelengths λ = 501-590 nm. Thus its center wavelength is λ0 = 546 nm and its bandwidth is ∆λ = 89 nm. This is very much like the Johnson V filter in the table above, so we’ll assume the same Fλ for G for the zero magnitude star:

and the tenth-magnitude flux F10 is given by

The telescope’s collecting area is a = 2700 cm-2, so

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12 2 10

13 2

3 92 10 W cm m 0 089 m3 5 10 W cm

F F . .. .λ λ µ µ− − −

− −

= ∆ = × ×

= ×

( ) 4 17 20 10 10 010 0 2 5log 10 3 5 10 W cm. F F F F . .− − −− = ⇒ = = ×

1410 9 4 10 WSP F a . .−= = ×

Examples (continued)

2. Atmospheric turbulence (seeing) blurs the images of stars taken with uncorrected ground-based telescopes, typically to a diameter of 2 arcsec at Mees. Suppose for simplicity that this image is uniform in brightness. How many pixels of the array does it cover?The solid angle of this 2-arcsec uniform blur is

and that of a pixel is

so the number of pixels is In reality, the seeing-broadened stellar image would be brighter in the

center and have a diameter between half-peak-brightness points of 2 arcsec, typically.

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22

seeing2 arcsec arcsec

2π π Ω = =

( )2 2 2pixel 0 224 arcsec 5 02 10 arcsec. . −Ω = = ×

seeing pixel 63N .= Ω Ω ≈

Examples (continued)

3. Suppose the star in Example 1 produces the image in Example 2. How many electrons are collected in each pixel of the star’s image in a ∆t = 100 sec exposure? By how many data numbers (DN) does the star’s image exceed the background sky level, in the displayed image?The total charge in the star’s image, collected within ∆t, is . Thus the number n of electrons in each of the N = 63 pixels is

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S SQ I t= ∆

( )( ) ( )( ) ( )

0

14546 nm 9 4 10 W0 96 0 6100 sec 24 electrons

63DN24 19 DN.

1 27

S S S

e e

Q I t Pn tNq Nq N hc

.. .hc

e. e

λτη

−

−−

∆= = = ∆

×= =

= =

See page 14 for other values.

Examples (continued)

4. With the telescope pointing 60 degrees away from a first-quarter moon, the moonlight produces a background observed – in blank, star-free sky – to be 50 DN per pixel in a 300-second exposure in the G filter. Show that this is much larger than the dark current accumulated in 300 seconds; then calculate the corresponding noise current, in electrons per second, within the size of the stellar image as in Example 2.

50 DN is n = 63.5 electrons, for a current in one pixel of The dark current per pixel at a CCD temperature of T = -20 C is 0.009

. So background dominates dark current. In N = 63 pixels, the noise current is therefore (see page 11):

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10 21 sec

e e e eN

N

e

q I q Nnq qI Nn

t t t tI .q

−

= = =∆ ∆ ∆ ∆

=

10 21 secB eI q . .−=

1sec .−

Examples (continued)

5. So what would be the magnitude of a star barely detected (S/N = 5) in the G image of Example 4?

See pages 10 and 12:

From Example 1 we know that the power collected from a zero-magnitude star is Thus – letting the barely-detected star be A and the zero-magnitude one be B in the magnitude equation –we have

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190

0

55 6 66 10 W.e SS NS

N N e

q PI hcIS P .N I hcI q

τη λτη λ

−= = = ⇒ = = ×

100 9 4 10 WS ,P . .−= ×

,0 ,02.5 log 2.5 log 22.9 .S S

S S

F Pm

F P

= = =

Next time

How to use CCDSoft to control the camera.

In particular, how to

• set the camera up for operation, including focusing the telescope;

• calibrate and use the autoguider;

• work efficiently using the Color data-acquisition mode.

Subsequent lessons on the data-reduction and image-prettification software, and on the optics and detection physics behind why the terms of the recipe are chosen.

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