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Photometric Calculations

Use of this program is free. Test-drive a demo version to try out the powerful features by clicking this icon.

Brightness Calculator -> Custom Exposure Tables

This program builds custom results in the same style as our simpler canned Easy Exposures tables. It outputs the same kind of table. Required input is more detailed, but is not restricted to "canned objects". It allows us to "roll our own" exposure tables. We can interconvert Apparent Magnitude, Brightness and absolute magnitude, but at least one still has to be known. The object's "apparent diameter" must be known for the viewing date, else, the program can calculate it from planetary radius and distance from the Earth. That kind of data is supplied by the Starry Night Pro program and similar resources; see Notes.

HELP consists of (a) a test-drive demo that walks you through the steps for several different "scenarios" - click the ? icon above - , and (b) more-detailed notes and formulas in NOTES on the bottom half of this page.

Usage: An asterisk (*) indicates data required for any calculation. An (OR) indicates two or more options are offered for data entry, and only one is needed. To resolve any conflict of extra entries, the program uses only the first non-blank field.

Custom object description:
Below, parameters are entered to generate a custom exposure table. These include object size and brightness, any magnification in use, any filters, and information about any camera coupling method being used. In most cases, choices are presented for setting up the calculation entries, depending on what is known and available.
Step 1. Object size*: Uses either published apparent diameter, or lets the program calculate it from Starry Night Pro or similar data -- given both radius in km, and distance from Earth in AU. Usage: Enter either (1a) apparent diameter method, or (1b) radius and diameter method (enter only one method):
(1a) Object's apparent diameter d:
       (point source = 1 minimum)
arc-seconds

(1b) (OR) program calculates, given
       object's
radius and distance
            (Starry Night Pro)

radius in km
distance in AU
Step 2. Brightness*: Uses current object brightness to fine-tune the custom exposure tables. Planetary objects vary considerably in apparent brightness, so published data for the night you are viewing may be preferable to a canned average value. Usage: enter only one of the three entry methods below:
(2a) object's total magnitude m
          (Starry Night Pro)

(2b) (OR) apparent magnitude m":
(2c) (OR) brightness B
m
m"
B
Step 3. Telescope: Uses telescope f-ratio to find the best row in a basic exposure table. With step 4, computes a total system f-ratio with camera, in combination with either an eyepiece or projection coupler. Usage: If telescope make and model is found and selected in the popup (3a), its f-ratio is used. If not found, select telescope's f-ratio manually in popup (3b).
(3a) select telescope:
Make Model f-ratio
(3b) (OR) select telescope f-ratio1:

Step 4. Magnification, positive projection, afocal coupling: This section computes total system f-ratio. The table stays the same for any given brightness and object size; the output row is highlighted that agrees with "total system f-ratio".

Usage: Supply both (4a) and (4b) for positive (eyepiece) projection. Supply both (4b) and (4c) for afocal coupling (camera lens). If (b) is blank, the program will ignore (a) and (c), and only use telescope f-ratio1. Enter eyepiece focal length (4b) manually in the text field, or browse and select popular eyepiece sizes by model in the popup.

Skip this step to get a system f-ratio for just the telescope (prime focus photography, camera body mounted directly to the back of the telescope; no eyepiece projection, no camera lens).

(4a) distance, objective to film plane (mm, positive projection)
(no camera lens)

s2
LEAVE BLANK if using a camera lens

(4b) eyepiece focal length (mm)
(OR) eyepiece focal length (mm)
(manual entry)

(popular models, pick by mm)
F2 by model
F2 by focal length

(4c) camera lens focal length (mm, afocal coupling)
FC
LEAVE BLANK if using eyepiece projection
Step 5. Filter Factor: This section computes the effect of a filter on Brightness to fine-tune the custom exposure tables. if using a filter, the popup supplies commonly used filters and their approximate filter factors. Orion's "Deluxe Stargazer's Filter Set" (cat. #5590) is used as a starting point. Factors are taken from Covington data in Appendix E. Usage: If using a filter for which no filter factor listing is found in the popup (5a), just manually enter its filter factor in the text box (5b). Skip this step to get a 'B' adjustment factor of '1' (no filter, no multiplier).
(5a) filter factor, common filters
(5b)   (OR) filter factor, other
           (manual entry)
Step 6: Camera type: "Reciprocity exponent" is automatically computed for film cameras when the exposure is over 1 second. Usage: check checkbox if the exposure table is to be used with film time exposures. See "Film vs. CCD" Notes for discussion and selection of best exponent for the popup, or leave 0.8 as an average factor.
check checkbox if film camera  (reciprocity exponent

The US Naval Observatory publishes MICA, software for PC and Mac, to obtain common astronomical data. You can Test Drive the software with a web version to obtain apparent diameter and apparent magnitude m" (select topocentric illumination calcs), and many other physical ephemeris. Date range is restricted on the USNO Web version.


Notes

The published Covington tables give us both surface brightness m" and photographic brightness B. For custom tables, for other objects or apparent diameters, we start the calculation with a B value. We may just convert m" to B as a starting point. Approximate formulas are:

Brightness

B = 2.512(9.0 - m")
m" = 9.0 - 10.086 ln B (natural log, to base e)

where:

B = brightness of object being photographed, as input or calculated.
m" or m-double-prime = surface brightness spread over one square arc-second

Given m" and the object's apparent diameter d, we can solve for a more appropriate value of B than with a simple conversion. Values of m" for the planets are in published data such as the MICA software program, or the Astronomical Almanac.

Apparent Magnitude and Apparent Diameter

m" = m + 2.5 log10(pi/4)(d2)
m  = m" - 2.5 log10(pi/4)(d2)

where:

m" = surface brightness spread over one square arc-second
m = total or "apparent" magnitude
d = apparent diameter, in arc-seconds
pi = constant 3.1415926535897932

Filter Factors

The custom program page corrects for filter factors when the value is supplied in the form. Otherwise a value of '1' (no filter) is assumed. The adjustment calculation (by hand, or by supplying in the form) is:

B (adjusted) = B/filter factor

A web-check of established amateur astronomy dealers indicates that this filter factor isn't published at all. For example, OPT and Orion both offer the #25A Red filter at "14% transmission". What does that mean?

We think it means 14/100 = 1/x, or x=7.14, which agrees closely with the industry Kodak Wratten values published by Covington. For a #25A, these are a filter factor of 8 for most films, or 3 for Tech Pan or CCD cameras. We build into the program the Kodak Wratten values, and we offer a choice for either film or digital camera.

How much of a practical difference between filter factor 3 and 8 is there? At f/10 ISO 25 if your shutter speed is 1/8 second for filter factor 3, it will be 1/4 second for filter factor 8. One f-stop's difference -- there's greater variation in the moon's surface brightness.

Solar filters are built with greater densities, often expressed as logarithmic densities. A filter factor of 1,000,000 (one million, or 1 x 106) is a logarithmic density of 6; 1,000 (1 x 103) is a log density of 3. Our One-Step program emulates the Covington published tables with typical solar filter factors of 1,000,000 100,000 and 10,000.

Film vs. CCD Cameras

Digital: In time-exposure situations over a few seconds at most, digital camera pixels are subject to thermal noise pixillation problems. These CCD's are optimized for daylight conditions. This causes white speckles or "fake stars" on the finished image. The Nikon D100 manual lists a conservative 1/2-second limit, though I have seen published D100 photos with longer values. Since each CCD has a unique "signature" pattern of affected pixels, some astronomers have learned to "mask" out CCD noise, though of course this does not recover the lost information in the masked pixels.

While lacking the megapixel and color depth of camera CCD's, a dedicated astrophotography CCD is built for long exposures in the night sky. CCD devices are not subject to "reciprocity failure" in long time exposures, but that is a moot point with digital consumer cameras if they are inherently limited to exposures of about a second or less. Good dedicated astrophotography CCD's still go for several thousand dollars, but they are MUCH "faster" than film.

Films: film is capable of exposures of hours' duration. Over exposures of about 1 second, it cumulatively starts taking more than 1 unit of light to expose the film by one more unit; "reciprocity failure" is a well known controlled variable in the film world. It is easily accounted for by the formula

t(corrected) = (t+1)(1/p) - 1

where

t is the exposure time (over 1 second)
p is a correction factor called the Schwarzschild exponent, typically 0.9 for newer slow films, 0.8 for older slow films or newer fast films, and 0.7 for older fast films.

Check the "film camera" checkbox if you want this calculation factor built into shutter speed results over 1 second.

Afocal Method (camera through eyepiece)

You can rig the camera to "see" through the eyepiece with a special camera mount (Orion SteadyPix™). Or, you can mount the camera on its own tripod and position it for the best view through the eyepiece. Or, (horrors!) you can snap a fast and dirty shot of the Moon through the eyepiece by hand. Always use a shutter release extension for steadiest results.

System focal ratio is the f-ratio of the telescope by itself, times the system magnification:

f = f1 x M

where system (total) magnification is the ratio of the two lenses, camera to eyepiece:

M = camera lens focal length FC / eyepiece focal length F2

So, if you had a 50mm eyepiece and a 50mm camera lens, the total magnification factor would be 1 x the telescope f-ratio.

Projection Method

"Projection Coupling" allows connecting the camera body to the telescope system through an extension tube and T-ring. This system is almost always connected to or through an eyepiece, affording magnification not available in prime-focus photography (which is taken at the telescope back).

Formulas for prime-focus photography are those for the telescope itself; the eyepiece "projects" the image onto the film plane, and this changes system f-ratio. We are using the formula

M = (s2 - F2)/F2;

where

M = projection magnification
s2 = distance from objective to film plane, i.e. 75mm
F2 = eyepiece focal length, i.e. 18mm eyepiece
FC = camera lens focal length in mm (if any)

How much of a deviation from the "ideal" exposure is acceptable? Covington notes that "a x1.4 difference is usually unnoticeable. Some films tolerate exposure differences of x8 or more." Our own early experiments with the lunar eclipse of 05-15-2003 bear this out!

What about my camera's f-stop? We'll quote Covington here: "The camera lens must always be wide open; you cannot adjust it to change the exposure."

I have an auto SLR camera. Can't I just use the built-in exposure metering? Yes -- if the object fills the viewfinder and if the light is strong enough for the camera's computer to allow the shot to be taken. This pretty well restricts this amenity to the Moon. Modern SLR computer exposure control is hooked to the lens to obtain f-stop (and lens or zoom f-ratio), and probably will not work at all without the lens. My Nikon D-100 locks up without the lens in prime focus photography, if I've forgotten to set it to Manual, which is easier for me anyway. The camera's computer has its own built-in set of f-ratio and brightness limitations; at best, we're "pushing the envelope" in night sky photography.

I have a nice digital camera with a non-removable zoom lens. Astronomy magazine regularly publishes stunning photos taken with consumer digitals. You'll note that most are brightly-lit compared to a black night sky: the Moon, aurora borealis, eclipses, twilight scenes. If your digital allows manual settings, so much the better, and exposure tables may still help you in any situation your camera's computer can't handle -- up to a few seconds' exposure time, anyway. OPT sells couplings to attach better digital cameras directly to the back of telescopes (wherever the eyepiece normally goes), camera lens and all. But, if the camera viewfinder doesn't "see" through the camera lens, focusing the telescope becomes a special challenge. Buy a book and see how it can still be done.

Our calculators will help you set up a custom Appendix A Exposure Table for an object when:

  • You know some of the variables, but need to calculate others
  • You know all of the variables, but some are different from the "canned" tables. For example, you have the published values of object "MARS", but you will be using a filter.
  • Or, you have the values, but by August 27th the apparent diameter will jump to four times average -- from about 6 to 25.1 arc-seconds. You want to know the effect on exposure time (answer: about one stop; not that much!)
  • You want to build an exposure table for a different object or one with different values.

Coding Notes

algorithm library (Perl subroutines)

 

 

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