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Revised rule for tripod shots using DSLR's and digital cameras.

By Joe Cali

A discussion on an astronomy forum in early 2013 discussed how long an untracked camera on tripod exposure can be left open before trailing becomes objectionable. Some authors of posts indicated they used a fixed time of 30s while others referred to the “500 rule.”

The old “500” rule states that –

Maximum exposure in seconds =                500               .
                                                        Lens focal length (mm)

These rules or formulae hark back to the days of film and were based on a set of starting assumptions about film grain size, size of print enlargement, viewing distance and resolution of the human eye.  They have been kicking around for a long time and I thought they were in need of an overhaul.

The 500 formula certainly works. However, the 500 rule is designed for an 8x10inch enlargement viewed at arms length. As a result, the formula often returns a exposure. These days, we often display screen-based images and images that are highly reduced from full acquisition size. The 500 rule returns very short exposure times.  While the resulting exposures do have very stationary stars, the indicated exposures are so short that there are not many stars and very few nebulae showing. 

When you take an exposure without tracking the motion of stars, the length of exposure is related to how much drift you find acceptable. So I've derived a revised formula, modernized for DSLRs that takes into account, final viewing size, size of the pixels in your camera and even a term to account for where you point the camera in the sky.

             max exposure time(s) =      [14*N*P]    .
                                                     [FL*cos(
d)]
where

N..........Number of pixels of drift*

P..........Pixel size (microns) (use value from table)    

Sensor Megapixels


Pixel size P (microns)
APS SENSOR


Pixel size P (microns)
FULL FRAME SENSOR

6 MPx

7.8

11.7

8 MPx

6.8

10.2

10 MPx

6.1

9.2

12 MPx

5.5

8.3

16 MPx

4.8

7.2

18 MPx

4.5

6.8

24 MPx

3.9

5.9

 

FL.........Focal length of lens (mm)

d.......... declination. Use the declination of the stars in the field that are closest to the celestial equator (the fastest moving stars) not the center of the camera field.

Cos (d) calculation notes :

If you don’t understand trig or don’t know what declination is, you can leave the term out of the formula. It just means that in some parts of the sky, you might be able to make a longer exposure but the formula will calculate a shorter exposure. You will still get stationary stars.  

You can also eliminate the term when using very wide angle lenses. They image such a wide range of declinations that the declination term becomes redundant.

The formula simplifies to : - 

max exposure time(s) =                 [14*N*P]    .
                                                           FL

Note that most computer software including MS Excel uses radian measure for trig functions. Divide the declination by 57.3 to convert to radian measure. [ = COS(d/57.3) ]

 

* To work out the value for n

To work out n for my formula look at any image from your camera before you take the pictures in Photoshop or similar program. View a full size image scaled to the screen size you want for the final display image and look at the scaling percentage you want to use for display.

1.5 x100 ÷ scale%   will give you a decent value for n.

You can also calculate it from pixel dimensions.

Example if you have a 24MPx camera and want to display a 1000x1500 image

24MpX Sensor has               4000 x 6000 pixels
Final display image  is        1000 x 1500 pixels

Scale factor = 4000/1000 = 4
n = scale factor x 1.5 = 6

But if

Sensor has 4000 x 6000 pixels
Display image 400 x 600 pixels
Scale factor 10
n=10 x 1.5 = 15

Example : Using a 14mm lens, 5 pixels drift, on an APS-C sensor with 5.4µm pixels pointed at the celestial equator
can take a 27 sec exposure. Pointed at the SCP the lens will see 45 degrees each side of the pole extends the time to 38 seconds.

The following table is calculated for the average DSLR, 12-16 MPx.
N= 5 Pixels trailing allows an image of 1500 pixels wide to be displayed -

ie a full screen image on a 20-24 inch monitor.

Generate

 Table

 ENTER=> Number pixels trail

7

ENTER=> DSLR Pixel size (µm)

4.8

 

MAXIMUM EXPOSURE TIME IN SECONDS

FOCAL LENGTH =>

10

15

20

30

50

100

200

300

400

Declination

 

 

 

 

 

 

 

 

 

0

47

31

24

16

9

5

2

2

1

10

48

32

24

16

10

5

2

2

1

20

50

33

25

17

10

5

3

2

1

30

54

36

27

18

11

5

3

2

1

40

61

41

31

20

12

6

3

2

2

50

 

49

37

24

15

7

4

2

2

60

 

 

47

31

19

9

5

3

2

65

 

 

 

37

22

11

6

4

3

70

 

 

 

 

28

14

7

5

3

75

 

 

 

 

36

18

9

6

5

80

 

 

 

 

 

27

14

9

7

85

 

 

 

 

 

 

27

18

14

 

 

Taking the pictures

Using the formula, work out the maximum exposure time for various focal length lenses you own.  Then prepare for your field trip.  Use the most solid tripod you can beg borrow or buy.  You will need some sort of shutter release.  Either a cable switch, infra red remote control. Some cameras allow remote control from a smart phone via an ap.  You can also use self-timer since all the exposures are usually less than 30 seconds.

All of the wide-angle example images were taken from at least 100km outside the city in dark country skies. Shooting from the city will result in fogged bright skies. You can get reasonably dark skies by travelling to the edge of the city and looking away from the city. The telephoto image just below was taken from the ACTEW water pumping station on Stockdill Drive at Holt which has reasonably dark skies when looking to the west across the Brindabellas. Lake George lookout (lower) has decent eastern skies and Namadgi, Tidbinbilla and the Cotter have reasonably dark southern skies. 

Examples

Eta_Car_fixed_tripod.jpg

The above image was taken with a 300mm f4 telephoto. 12 pixel trailing was allowed because the image was only ever going to be displayed at 12.5% scaling.

N = 100%÷12.5% x 1.5 = 12 pixel trail.

max exposure time(s)        = [14*N*P] / [FL*cos(d)]

= 14 x  12 x 5.5 / [300 x cos (40)]

= 4s

At ISO 12500, four exposures of 4s were made in rapid succession aligned and stacked to produce the above image. The effective exposure is 16s. If you want to learn how to stack images in photoshop, Google “stacking astro images in photoshop” and you will get dozens of links to videos and web pages describing the process some with Adobe Photoshop some with other software.

Geoff's Knob Survey-5848.jpg

Above Image taken at ISO 25600 17 mm  f/2.8  15s   Below Image taken at ISO 800 12 mm   f/4  300s tracked with Astro Trace tracking. The high ISO image has more noise while the low ISO  tracked image has tracking errors and artefacts. Images captured in raw and processed in Lightroom.

Geoff's Knob Survey-5853.jpg

 

INNAMINKA-2016.jpg

Image above taken at ISO 3200 50 mm  f/1.7  8s exposure. Raw capture + Lightroom processing.  Years ago, such an image would have required up to 60 minutes precision tracking. I captured four identical 8s exposures in rapid succession at the same time as the image above. In the image below, the four exposures were stacked up as layers in Adobe Photoshop. The images were aligned to cancel out star movement from image to image then the images were added together to make a longer exposure.  The addition of 4 images results in the added benefit of averaging and cancelling out of noise resulting in a smoother as well as brighter image. Image has also had adjustments to brightness and colour saturation to enhance nebulae.

INNAMINKA-2020 750px.jpg

 

INNAMINKA-2036-Edit.jpg
The above image was taken with an ultrawide angle lens.
 
ISO 12800 10 mm f/3.5  20 s  Image captured in raw and processed in Lightroom.

 

Don’t be afraid to experiment and have some fun!

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