Numerical Aperturecalculator

so that you can see that your measured numerical aperture is going to be proportional to the input beamwidth. So the manufacturer might be foreseeing an input beamwidth of $W$, whereas you might only be giving it $W_0$: the outcome is obvious from the drawing.

Polarization of light is a property that applies to turning waves that shows the geometrical blooming of the oscillations. In a turning wave, the way of the ...

Vivitar TX mounts look very similar to T4 mounts but they are not fully interchangeable.   T4 mounts can be used on TX lenses but TX mounts can not be used on T4 lenses.   TX mounts have slightly better automation.   T-Mounts thread onto telescopes, mirror lenses and preset lenses.  They do not offer any automation.   T2 mounts are adjustable T-Mounts.

Numerical apertureand resolution

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The Edixa m42 mount is oriented slightly off of the Praktica standard.  Lenses with aperture arms and automatic aperture lenses made by other mfg's will not work properly on an Edixa body.  Also, Edixa lenses may not work properly on standard m42 bodies.

Miranda's lens mount was originally a 44mm screw mount.. They switched to a bayonet mount for the Sensorex.  Some of their lenses have both mounts so they can be used with any Miranda body.

Tamron Adaptamatic mounts attach to the lens a bit awkwardly and are tightened to the lens by way of a large retaining ring.   Adaptamatic mounts offer limited automation and can be tricky to attach.   Tamron replaced the Adaptamatic with the Adaptall system which offers more control and is much easier to attach.

Numerical aperture ofobjectivelens

Petri only made one lens mount, but they also used M42 mounts.  Some Petri lenses have Pentax K mounts but they were made by third party manufacturers such as Cosina.   Petri bayonet and M42 mount lenses were excellent.   The Cosina made lenses are not the same build quality but the optics can be quite good.

Numerical apertureformula with refractive index

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Sigma YS mounts are basically T-mounts with an aperture pin.   They are adjustable and must be adjusted to achieve proper alignment of the aperture pin.

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Topman made lenses in the early 1980's.   They used an aperture specific interchangeable mount.  These mounts are rare but not in high demand,.

Some modern objectives have very wide beamwidths indeed: this makes for very long working distances / focal lengths whilst achieving high NA. Depending on your laser, your beamwidth may only be less than a millimetre (I'd say this is more than likely), whereas I think Zeiss and Olympus use about a 6mm beamwidth and Nikkon have even given up on the standard "Royal Screw" (Royal Microscope Society RMS thread) used for over 100 years as a standard to hold objectives on microscope turrets with and chosen instead to use much bigger bores and I think their beamwidth may be approaching 12mm.

Tokina lense, made in the 1960's, used an interchangeable mount similar to a T-mount.  The mount was 47mm threaded.  Don't confuse it with a Komura 47mm mount.  These lenses and mounts are rare.  These are also called Hanimex H mounts.

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Numerical apertureformula

All objects radiate energy, but some wavelengths within the electromagnetic spectrum are invisible. Detectors in an infrared camera capture a particular range ...

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NOTE: Don't mistake T-mounts, T2 mounts and YS mounts for M42 mounts.   They are all 42mm but M42 has a different thread pitch.  They are never compatible with each other.

The Sigma mount has two variations.  The first version has two bayonets to support heavy lenses.   That feature was not actually used so they removed the extra bayonet with the introduction of the SD14.  All Sigma AF bodies use the Sigma bayonet mount.  Early Sigma MF bodies used Pentax mounts.

The Argus 21 50mm f3.5 Cintar can be removed and used as an enlarger lens.  It is not the same mount as the later C lenses.

Using a laser setup, I was asked to determine the aperture of a given lens and then use some geometrical arguments and compare the theoretical value from the manufacturer and the experimental value. However, when I did this, the values differed by orders of magnitude. The way I got the aperture was to let the laser light pass through the lens onto a white screen and then keep the screen at a fixed distance from the lens and measure the radius of the light spot obtained. Then I used geometry to determine the angle and thus its sine. Could diffraction be the reason of such a large error?

It sounds as though you might not have "filled" the lens properly. An infinite conjugate microscope objective, for example, has a specified numerical aperture when it is driven by for a collimated beam of a specified beamwidth and apodisation (i.e. whether Gaussian, uniform or so forth). See my drawing below:

Extension distortion, also called wide-angle distortion, is when objects close to the camera appear unnaturally large (or far apart). This effect is especially ...

Numerical aperture ofoptical fiber

The Fresnel or Dielectric Fresnel node computes how much light is reflected off a layer, where the rest will be refracted through the layer. The resulting ...

Komura used two interchangeable mount systems.   The first was a 47mm threaded adapter similar to a T-mount.  It is called a Unidapt.   Do not confuse this with a rare Tokina adapter which is also 47mm.  The second system is called Uni Auto.  It is a bayonet system similar to Tamron Adaptall.   Both adapters can be very hard to find.  This pic was borrowed from a forum.

Otherwsie, the simple measuring of numerical aperture as you have is in general not meaningful, even if you do fill the lens until you can't get any more light in, i.e. vignetting limits your input beamwidth. Manufacturers do NOT mean that the sine of the angle of the output light cone is the NA when the input fills up all the available space. What they mean is their objectives will achieve the rated aberration performance when they are filled such that the output lightcone is the quoted NA. Practically, you can often fill a lens a great deal more that its rated beamwidth, so if you measure NA by filling till you see vignetting, you may get an overly high value. Yes the lens can output this high NA, but it won't be meaningful for imaging because the aberration performance will be crap in this case.

You also need to be very careful of NA measurements with lasers because they output Gaussian beams whereas manufacturers generally talk about their specifications with a uniformly apodised beam. If you use a Gaussian beam, work out numerical apertures using the $1/e^2$ beamwidth, i.e. the diameter of the beam where its intensity has fallen to $1/e^2$ of its peak, on-axis intensity.

Numerical aperture ofmicroscope

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