Re: Pinhole Calculations

photoian@earthlink.net writes:

> Query to Larry Bullis:
>
>
> I have experimented with a set of 12 pinholes obtained fromCalumet, ranging
> from 0.0059 to
> 0.032 inches in diameter, on a 4x5 view camera.
> It quickly became apparent that angle of view is dependent only only on
> lens to film plane
> distance. Any of the 12 varying pinhole sizes give the same angle of view
> at a given bellows extension.
> The difference is in the amount of light admitted by the pinhole aperture.
> Thus it makes sense that, as
> the pinhole aperture becomes smaller , admitting less light, the bellows
> extension must decrease, to
> maintain the same amount of light, which means the focal length gets
> smaller. You've given a formula
> to calculate the optimum pinhole size for a given focal length to give the
> "sharpest image."
> The formula is pinhole(in) = square root FL x 0.0073 or pinhole(mm)= square
> root FL x 0.03679.
>
> My question is; does this formula really give the sharpest image?
>
> First, you've said that depth of field is essentially uniform from near to
> far and somewhat soft
> because of diffraction. Since, for a given focal length, aperture(pinhole)
> varies inversly with f-stop, the
> formula must be designed to balance pinhole against f-stop, one admitting
> more light and the other
> admitting less light. The constant (.oo73 or .03679) is what determines the
> answer. So, now the
> question is; How is the constant determined? Does it give the "sharpest"
> image or is it just a trade off
> between exposure time and pinhole size? Do smaller pinholes give more
> diffraction and thus less sharp
> images? Using a different constant will gives different answers; what is
> unique about the given
> constants?
>

    1. You are right in observing that the angle of view depends only on the
        distance from pinhole to film, and has nothing to do with the size of
        the pinhole. The easiest way to visualize what is happening is to make
        a scale drawing of the camera, showing the film plane and the pinhole
        at the desired distance from the film. Straight lines drawn from the
        edge of the film through the pinhole show you the angle of view. Note
        that the intensity of light from the pinhole does fall off as you move
        from the center of the film toward the edge of the film, both because
        the film get farther from the pinhole, and because when viewed from an
        angle, the circular pinhole looks more and more elliptical and has a
        smaller effective area.

    2. The calculation for 'optimal' pinhole usually starts with some
        assumption about the physics of light going through a small hole.
        Since every aperture, hole or lens, produces a diffraction pattern, one
        'rule' is:

            The size of the optimal pinhole for a given focal length is the
            size of the diffraction disk it produces.

        The theory behind this rule is that a larger hole would produce a
        larger geometrical beam of light coming through, and therefore a less
        sharp image, while a smaller hole would produce a larger diffraction
        spot, and therefore also produces a less sharp image.

        Note that the size of the diffraction disk depends on the wavelength
        (color) of light. One common assumption is to assume a wavelength of
        500 or 550 nanometers (nm). This is a green color. If you use
        panchromatic film, red light coming through the pinhole will make a
        slightly larger diffraction spot. But nothing is is very critical
        here.

        Nothing in this rule takes into account the f number of the pinhole.
        The f number is just something that results from computing the optimal
        pinhole for a desired focal distance. Because the optimal pinhole size
        increases only as the square root of the focal distance, the f number
        gets larger and larger as the focal distance increases.

    3. Since you have a number of pinholes, you can try some of them at a
        fixed focal distance and what happens. Please report on your findings.
Received on Mon Mar 11 10:28:03 2002