Pinhole Photography: Formula for Calculating the Best Aperture in Microns, Infinite Depth of Field, and Conversion When the Ultimate Reciprocal Law Fails

1. The physical paradox of pinhole imaging: The smaller the hole, the clearer it is!

In pinhole photography, the diameter of the small hole has an extremely precise optical limit:

1. The tug-of-war between geometric optics and wave optics:

• When the aperture is too large: The beam cannot converge, each object point forms a huge geometric circle of confusion on the film, and the picture is completely blurred;
• When the aperture is too small: The strong Fresnel single-hole diffraction (Diffraction) is completely dominant. When the light passes through the edge of the tiny aperture, it is severely bent and diverged. Not only does the sharpness of the picture not improve, but it completely atomizes and collapses!

2. Rayleigh’s mathematical formula for optimal pinhole diameter (Lord Rayleigh Equation):

• ( d = 1.9 imes \sqrt{\lambda \cdot f} )
• Where ( \lambda ) is the central wavelength of visible light (about 0.00055mm), ( f ) is the focal length of the pinhole to the film (depth of the camera obscura);
• Classic Practical Benchmark: If your camera obscura focal length is 50mm, the calculated optimal pinhole diameter is exactly 0.31 mm!

2. Self-made high-precision micron pinhole nanny-level process

Pricking a hole randomly with a pin will cause edge burrs to seriously damage the image:

1. Material preparation: can aluminum skin (sanded to a thickness of 0.1mm) or brass sheet, fine sewing needle, 1000 mesh ultra-fine water sandpaper;
2. Indentation and back grinding method:

• Gently press the tip of the needle vertically against the metal piece and twist until a small point is slightly raised on the back (do not puncture!);
• Place the metal piece flat on the sandpaper and add water to carefully polish the raised points on the back until the metal is worn through to reveal a tiny circular pore;
• Check under a high-power magnifying glass or film scanner: the edges of the pores must be as smooth and round as a razor, absolutely round, with zero burrs!

3. Actual conversion of f/200 ultra-small aperture photometry and reciprocity failure (Reciprocity Failure)

1. Calculate equivalent aperture value:

• If the focal length is 50mm, the aperture is 0.25mm, the aperture F value = 50 / 0.25 = f/200!
• Compared with the standard f/16 aperture, the amount of light entering is attenuated by 8 stops (256 times)!

2. Quadratic nonlinear time penalty for reciprocity failure:

• Measured with a mobile phone light meter, it takes 1/4 second at f/16;
• Extrapolated to f/200, the original exposure should be 64 seconds;
• Fatal Trap: Under low-light exposure for up to 1 minute, the extremely strong reciprocity law of the film fails, and the actual exposure time must be extended to 4 to 6 minutes!
• Pedestrians and cars on the road completely evaporate and disappear in a long exposure of several minutes, leaving only static buildings and smoke-like clouds, presenting a dreamy sense of frozen time.

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