Pinhole camera modelling

Topic:Functions, Geometry, Linear Functions

Applet designed to be displayed on a 10" or more screen. A pinhole camera is a device which creates an image on a surface through a small diameter circular aperture without any optical element. This pinhole camera modelling allows to customize all the device parameters dynamically:

Pinhole diameter
Wavelength
Pinhole-sensor distance, improperly called focal length
Subject distance
Sensor size

Bottom panel shows how a ponctual object creates an image spot on the sensor through the small diameter circular aperture according to geometrical optics rules. However the real life experimetation shows a different behaviour since light is a wave and going through a pinhole leads to make the beam diverging more than expected according to geometrical optics rules. This is called diffraction. Top panel shows evolution of the image spot diameter on the sensor according to geometrical optics rules (blue curve) and wave optics rules (red curve) Diffraction spot diameter and geometric spot diameter don't vary in the same way depending on the pinhole diameter. In order to get the smallest actual image spot, a trade-off is found by minimizing both values. So the best pinhole diameter can be determined by the position of the intersection point. Try several configurations (close or remote subject, long focal length or wide field of view, wavelength, etc.) and check how it influences the best pinhole diameter value. This is a perfect pinhole camera modelling since the pinhole thickness is null. Of course, an actual pinhole will be several micrometers thick and the aperture won't be prefectly circular with clean edge. All theses flaws would affect resolution, contrast, luminosity, field of view, etc. You can slide and zoom in order to focus on a detail or get overall view. The object point can be moved manually and the "Subject distance" field allows to place it very remotely and bring it back without zooming and dezooming. Any question or remark ? Feel free to leave a comment thanks to the share button in the top right corner of this page :)

A simplified formula is usually used to determine the best pinhole diameter for a given focal length:

Will you find under which contitions this formula is true ?

Pinhole camera modelling

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