As was stated in chapter 4, "The Exposure Base", the near-point/far-point separation difference, in short: "deviation", is not a constant, but rather a professional agreement. If, however, one agrees to use the 1/30-rule and the value derived from it for  = 1.2 mm for miniature formats and approx. 3 mm for a format of 2x 6x6 (6x13), as one has for amateur stereo photography, it must be held constant within the equations. If one wishes to use other values, i.e., for photogrammetry, the graphs 1 - 3 should not be used, but should instead be taken from the ladder table, graph 6 (see appendix).

Prerequisite:
Deviation = constant
b_N - b_F =  = constant

For simplifications, assume:

b_F = b_O

The triangle with the opposite angles  are similar, therefore:
 

bO

=

(= tg )

2 * aN

2 a'

1

1

bO *

=

*

aN

a'

1

1

1

1

1

1

=

-

;

bO *

=

* (

-

)

a'

f

a

aN

f

a

1

1

bO

=

* aN * (

-

)

f

a

aN

aN

bO

=

* (

-

)

f

a

aN

aN

assume

= 1

;

bO

=

* (

-

1)

a

f

Since the value of a', the image distance in the camera, can hardly be measured, it is replaced with help of a well-known optical formula.
The assumption: a_N/a = 1 distorts the result only ever so slightly. With a large amount of depth of field t_s, a can be significantly larger when a_N is big.

The value a_N/f then is very large. With a small a_N the value of a, the object distance = focal range, is not much larger, since then the depth of field t_s, dependent on the aperture, is also not large.

The value of a_N/f is then small too. Subtracting 1 or 0.8, for example, makes no difference.

According to the above equation, the stereo base b_O is dependent upon the selected stereo window distance from which  is derived, from the focal length f and the near-point distance a_N.  and usually f are constants so that only the near-point distance remains. The far-point distance is not of importance and must be considered in the choice of the aperture.

If one calculates the enlargement factor V from the known formulas for the focal length f, object- and image distance a, a' and substitutes them into the equation for the calculation of the base, this equation simplifies to b_s = /V.

Since both the depth of field and the exposure factor are dependent on the enlargement factor, all the relations can be depicted on graph 4. This is of special interest to macro- and micro-stereo-photography, where a lot of work involves the enlargement factor. Graph 5 shows the base dependent on the enlargement factor with different focal lengths = picture diagonals.
 
 

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Last modified on January 18, 2004

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