- Zemax Pinhole Diffraction
- Pinhole Diffraction Method
- Pinhole Camera Diffraction
- Circular Aperture Diffraction Equation
Pinhole, more specifically, to observe the interference and diffraction that occurs due to the pinhole and to successfully achieve CCD camera recording of a projected diffraction pattern from a pinhole. This experiment involved the diffraction of a laser incident upon a 100- m diameter circular aperture. The ideal pinhole camera would have an infinitely small hole. The smaller the hole, the bigger the sharpness, until the limit of light diffraction (that also affects glass lenses). Such a small hoje poses a problem: too little light enters the camera, and the picture takes forever to be shot.
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|A laser beam passes though a pinhole in aluminum foil, producing a circular diffraction pattern. (Disc 23-7, 16 sec.)|
Zemax Pinhole Diffraction
Pinhole Diffraction MethodBackHow is the diffraction pattern of the Airy Diskformed?
How does the diffraction pattern known as the Airydiskget generated by shining light through a pinhole? Or moregenerally,what causes diffraction of light? Diffraction of light occursbecauseof its transverse wave nature. We have already said that whenlighthits an object, it is diffracted. This phenomenon is bestunderstood by an examination of Huygens' Principle. In 1678, the Dutchpysicist Christiaan Huygens wrote a treatise on the wave theory oflight in which he presented a theory now known as Huygens'Principle. It states that every point ona wave front can be thought of as a new point source for wavesgenerated in the direction the wave is traveling or beingpropagated. OR-- the wavefront of a propagating wave oflight at any instant conforms to the envelope of spherical waveletsemanating from every point on the wavefront at the prior instant (withthe understanding that the wavelets have the same speed as the overallwave). Fresnel later elaborated on Huygens' Principle by statingthat the amplitude of the wave at any given point equals thesuperposition of the amplitudes of all the secondary wavelets at thatpoint (with the understanding that the wavelets have the same frequencyas the original wave). These are termed Huygens’ wavelets. The formation of the Airydisk can best be described by looking at how imaging of a luminouspointoccurs in a lens system such as is found in the compound microscope.Thefollowing diagram shows what happens.
Pinhole Camera Diffraction
If a luminous point at A is projected through thefrontlens of an objective O1, and assuming that the light ismonochromatic,light coming from point A will define wave surfaces as spheres (e.g., So)with their centers at A. Assuming the objective to be a perfectlens,the light going through it will also produce wave surfaces as spheresaswell (e.g., Si).The centers of these spheres are at point A'0which is a geometrical image of A.<>At any point on the wave surface ofSi according to Huygen's Principle, the image A'0is formed as if all the points of the wave surface were actual sourcesof light with the same vibratory state. But any point on the wavesurfacesuch as M emits vibrations not only towards A'0, but also inother directions. In fact all the points on the wave surface Sidiffract the light which spreads over the image surrounding the point A'0. The diagram below at the left shows that all the vibrations emanatingfromany point on the wave surface Si will reach point A'0in the same vibratory state. Only two waves from points M and M0are shown to keep the figure simple. As the waves have thesame vibration, the amplitudes are additive and since amplitude is seenby the eye as brightness, at point A'0, we have a verybrightspot.
Thediagram on the right shows vibrations going to a point A'1fromM and M0. The amplitudes are opposite each other when theyreachthe plane (indicated by line P and extending out from the page) whereourdiffraction image is generated. We would now have a dark area atpoint A'1 because the luminous amplitudes cancel each otherout and add up to zero. The same situation would happen if A'1were on the other side at the same distance from A'0. And in fact if one considered the whole plane of line P as shown by thesquare in perspective, the image would be a dark ring with a radius A'1-A'0with A'0 at the center as shown by the circle. Ifthe vibrations coming from points M and M0 were imaged at apoint A'2 on line P twice as from point A'0as A'1, the amplitudes of the vibrations would once again beadditive and one would then see a bright ring in the plane of lineP. It also follows that the intensities of the vibrations at all thepointson the plane of line P results from vibrations from all the points onwavesurface Si, not just those from points M and M0.
If all this information is taken together, then theimageseen in the plane of line P would be a very bright central circulardisksurrounded by alternately bright and dark rings whose intensitydecreasesrapidly as distance increases: the Airy disk. It canalso be seen that the distances between the bright and dark rings willchange with changes in the wavelength of light.
It must be remembered that any object observed inthemicroscope is subject to the phenomena described here and this hasimportantconsequences for the generation of enlarged images in the microscopeandis why the concept of numericalaperture is so important in microscopy.
*Diagrams redrawn from Francon, M. 1961. Progressin Microscopy. Pergamon Press: London (also Row, PetersonandCo.: Elmsford, NY).