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HAND COMPUTER
( Written 1984) 

READ THIS NOTICE
This Hand-Computer has been designed for scopes of 6" aperture.
For others apertures it is necessary to change the parameters.
For a more versatile one, a fourth disk must be added.

One of the problems that I had to resolve when I began to photograph the planets was the determination of the exposure-time.

Contrarily to how it could be thought, in fact, also the TTL photometers of the modern reflex cameras have not practical application in this field, since, to being able to work well, they should have a very little spot-reading of some square millimeter.

From here the need to create an instrument able to supply the necessary data. 
The result is the Hand-Computer described and illustrated here.

Conceived in shape of disc, it is capable not only to supply for the planets, but also for the Sun and the Moon, the correct exposure-times, according to the film-speed and to the focal-ratio of the optical system.

For the planets, the disc supplies also, with good approximation, the reproduction scale, that is, the diameter in millimeter of the planet in the focal plane of the telescope. For the Moon and the Sun this data are not necessary, being it good known to every amateur (approximately 1 cm. for m. of focal length).

From the reading of the disc there can moreover be found:

Ø The focal ratio corresponding to every focal length;
Ø The focal length corresponding to every focal ratio;
Ø The values of the relative resolving power (expressed in lines/mm) for every focal ratio;
Ø The brightness-relations among the various Moon phases;
Ø The brightness-relations among planets;
Ø The brightness-relations among the planets and the Moon-phases;
Ø The filter-factors for the photography of the Sun with ND filters (photosphere);
       Other useful indications on the back of the disc.

The reproduction-scale could be easy determined, since between angular diameter of the planet, linear diameter of the planet on the focal-plane, and focal-length in use, exists a linear and direct proportionality. The formula that allows to calculate with precision this diameter is the following: 

where the number 0.004848 is the result of the operation:

Since the angular diameter of the planets varies according to their distance from the Earth, the disc gives only approximates values, for the more favorable period (that one of the opposition for the external planets, that one of the greatest brightness for Venus, and that one of the transits for Mercury).

Since the planets Jupiter, Venus and Saturn (rings) have similar diameters, I assumed for all the value of 40 arcsec., that supplies the scale of reproduction with good approximation.

More laborious was instead the solution of the problem relative to the exposure time. To such aim they have been taken in consideration:

Ø The amount of light that the planets receive from the Sun according to  
        their distance from it, placing Moon = 1;

Ø The albedo of every planet and of the full-Moon.

As indicated on tab.1, the relation between albedo and lighting allows to calculate the brightness of a planet or moon (amount of light reflected from the planet for square angle).

Once established the brightness-relations of a single planet (tab.2), the better thing to make is to determine empirically the correct exposure-time for one of they (for ex. the full Moon). Those necessary for the other planets are then an immediate consequence.

It  is opportune to keep in mind that the exposure-time can be influenced also from other factors, as for ex.:

Ø transparency of the sky in a done place and/or moment;
Ø height of the planet on the horizon;
Ø transmission- and/or reflection power of the optical system, etc.

It  is also important to keep in mind that the ideal film does not exist, since in our case it should be superfast and grainless.

The low speed of a film is not always a disadvantage, as for ex. in the Sun-Photography, where the low speed returns quite useful. One of the best films for this use is the well known Agfaortho Professional 25 (25 ASA = 15 DIN) that, next to its low speed, offers optimal contrast and high resolution (350 lines/mm).

An ND filter (Neutral Density) is however always necessary. The transmission-power of a ND filter expresses with a power of negative exponent (for ex. 10^-3 for a filter that transmits only 1/1000 of the incident light, that it is simply indicated with ND3).

Such filters must be chosen in such an way that exposure-time of 1/1000 sec. or shorter are possible, with the aim to diminish the deleterious effects of the turbulence and the moved images with large focal-lengths.

The turbulence of atmospheric origin is reduced… going in some mountain; that one of instrumental origin making so that the light enters in the telescope already attenuated (full aperture filter, or off-axis filter on obstructed reflectors ).

In the lunar- and planetary photography, instead, one must always conform himself with compromise-solutions. The resolving power of films and theirs speed are in fact inversely proportional, and improving the one becomes worse the other. If such proportionality were linear, a combination would be equal to the other. On fact, however, it is not so, and it is necessary to analyze which it is the best compromise. That can be done by tracing ( diagram ) an ideal curve (a hyperbola in a diagram with arithmetical scale, or a straight line in a diagram with logarithmic scale) that represents the course of the resolving-power according to the film-speed, taking as comparison-term a real film (in our case Agfapan 400 or Kodak TriX). Representing then on the diagram the other films in commerce, one can see that few films coincide with the curve, being worse, regarding the reference film, those to the under and to the left of the curve, and better those to the over and to the right of it, having higher resolution by equal speed, or higher speed by equal resolution, and approaching so itself to the ideal film.

Such is the case of the Kodak Technical Pan 2415 (TP 2415), that is truly extraordinary for astronomical use, especially if hyper-sensitized with forming gas, catching up a speed of approximately 24 DIN and conserving a grain comparable to that one of a15 DIN film (as they indicate, but only accidentally, the digits 24-15; a good mnemonic rule!). In effects, its resolving-power is approximately 320 lines/mm (similar to Agfaortho 25). Very important to keep in mind, by choosing the combination film/focal-length, is the relation between the resolving-power of the optical system in lines/mm ( tab.3 ) and that one of the film. In fact, it would be foolish to use, for ex., a 2415 film of 320 lines/mm, with a focal ratio of f/90, that would give no more than 18 lines/mm. This, at least, from a theoretical point of view.

Practically it is always difficult to integrally take advantage of the resolving-power of the films (what can be obtained only in a laboratory, in ideal conditions of employment). For this, the resolving-power of the films must always be considered smaller, with a consequent shift towards left, in our diagram, of the films of fine grain, being the greater shift for the high resolution films. To the limit, this could shift these films under of the curve, with the consequence that the better films would then remain those of the type AGFAPAN 400 / Kodak TriX, with good speed, whose resolving-power of approximately 100 lines/mm can be taken better to advantage.

In order to take advantage of the resolving-power of the films, it is opportune that the one of the optical system is at least two times higher. With a 400 ASA film, for ex., with its resolving- power of 100 lines/mm, a focal ratio of f/8 (200 lines/mm) or f/11 (150 lines/mm) would be advisable. The exposure-times would so be shorter – due to the greater brightness of the optical system - with obvious advantages.

But the resolving power is not all: 
great importance has also an other characteristic of the films, known as acutance. This quality is intimately connected to the phenomenon of the light-scattering, and is more emphasized in the thin-layer films. There are however in commerce special developers to exalt the acutance (Beutler, 50 Kodak DK Mod, Crawley FX-13, etc).

For the Moon-Photography exists, at last,  the problem of the different and unequal brightness: border/terminator (by first and last quarter), and day/night (ashgray-light ).
Although this problem can be resolved partially in the darkroom, with the aid of masks, interesting results could be obtained with the relatively new film AGFAPAN VARIO XL, that has an extremely wide exposure-latitude. Beyond to this, this film has a high speed (until 33 DIN=1600 ASA) and, above all, an excellent relation grain/sensitivity, for which it should have a special place in our diagram.

In order to complete the outline, have a look to tab.4,  tab.5 and  tab.6, containing other useful data for this purpose, and to the image of  the three discs of which the Hand Computer is composed.

There is still experimenting what remains. The "computer" will aid us, but you must not preoccupy ourselves: we will find always enough difficulties. But perhaps is better so; otherwise, which merit would we have?

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