T3D Re: geometry of a MF macro camera

[john bercovitz <bercov@xxxxxxxxxxx>]

I see Greg is thinking along the same lines I am.  Going to a
smaller format doesn't help you on maofd because maofd is just
1/30 th of the distance from the lens to the film regardless of 
format size.  Where the smaller format helps helps you is where 
depth of field is your problem.  So let's do a DOF comparison 
of 35 mm format and 4x5 format.  4x5 format is about 4 times the 
size of 35 mm, linearly speaking, and so I will treat it as such.

Let's try 1 part in 2500 (1.4 minutes of arc) for the resolution,
both geometric and physical.  So we need a linear aperture of 
1.9/1.4 = 1.4 mm.  This is regardless of format because the number 
1.9 is for angular resolution and angular resolution is what stereo 
people care about since they view from approximately the center of 
perspective or suffer the consequences.  Another way of saying this 
is that angular magnification is always constant and is equal to 1 
regardless of format.  Linear magnification will be quite different 
between formats.

For 35 mm format, let's use a 35 mm lens on the camera and focus 
it out 5 mm and use a 40 mm focal length for our viewer.  That
means the sharpest focus in object space is 280 mm from the lens.
So 280 mm is the perspective our camera has on the object.  The
f/number on the barrel of the lens is 35/1.4 = f/25.  From geo-
metric optics, the depth of field is from 259 to 304 mm for a
range of 45 mm.  Field of view is the diagonal of the format 
divided by the distance from the lens to the image = 40/40 = 1.0

Now let's go to 4x5 format.  The distance from the lens to the object 
stays at 280 mm to maintain the same perspective.  We need to cover 
something 4 times as big so the distance from the lens to the film is 
now 160 mm instead of 40 mm.  From 280 and 160 we see the lens focal 
length is 102 mm.  Field of view is still 1.0 (160/160).  Again we use 
the same linear aperture of 1.4 mm to maintain the physical optics 
resolution.  The f/no is then 102/1.4 = f/73.  And when I check the 
DOF geometrically, I find that it is from 259 to 304 mm!  Yikes!  
I musta lied!

I'll look into this further and get back to you.  It is true that 
if the aperture gets small enough, the hyperfocal distance gets very 
small and the acceptable far point goes to infinity but that's not 
the situation here.  We don't have infinity in a macro.  I gotta 
think on this one.  Maybe it's such a minor effect at this distance 
that it doesn't matter.

John B


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