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Numerical apertureof objective lens

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In this metering mode, the camera uses light information from the entire scene and creates an average for the final exposure setting, giving no weighting to any particular portion of the metered area. In some situations, such as a snowy landscape, this mode will result in underexposure by 2 f-stops or more, because the metering system attempts to darken an excessively bright scene.

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Often times when starting the design process one can inadvertently request conflicting specifications. This example will show how easy this is to do and how to avoid it when specifying a lens.

Numerical aperture meaningin optical

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So what if the customer needs a numerical aperture of 0.25? To get this, at least one of the other specifications need to change. To do this, lets start with the initial specification for NA=0.25 and find what the f/# would be using this spec.

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Some cameras allow the option of locking exposure when autofocus is achieved. In other cameras the AF point is not used for exposure calculation, and in such cases it is common for metering to default to a central point in the viewfinder, using a pattern based on that area. There is considerable variation among different manufacturers how multi-zone metering is implemented–even in the model range of the same brand–and how much priority is given to the AF point itself. Some "Scene" modes, such as sunset, sports and night exposures also often affect the calculations of this metering pattern.

Now we can find the focal length of the lens by assuming that the customer wants entrance pupil diameter to stay at the specified 20mm.

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Numerical aperture (NA) refers to the cone of light that is made from a focusing lens and describes the light gathering capability of the lens (similar to f/# ). NA is defined by the following equation, where n is the index of refraction of the medium (often n=1 for air), and α is the half angle of the cone of light exiting the lens pupil.

Numerical apertureof optical fiber

Below are three sets of lens specifications that would result in the desired system NA. There is an infinite number of specifications that will give the desired NA if one is allowed to change more than one spec.

In this system, the meter concentrates on the central 60–80% of the scene. The balance is then "feathered" out towards the edges. This mode of exposure is less influenced by peripheral areas of the scene and is therefore well suited for photographs with subjects or objects of interest in the central part of the image. Some cameras allow the user to adjust the weight/balance of the central portion to the peripheral one. If the camera allows a user to move the focus point off the image center, metering will occur around the new focus location. Although promoted as a feature, center-weighted metering was originally a consequence of the meter reading from the focusing screen of SLR cameras. Light scatter from the focusing screen and proximity of the meter cell caused less sensitivity at the edges.

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Spot metering is not influenced by other areas in the frame. It is commonly used to shoot very high contrast scenes. For example, in a backlit situation a rising sun may be behind a person whose face will be much darker than the bright halo around the body and hairline. Spot metering allows the camera to measure the light reflected from the person's face and expose properly for that, instead of adjusting exposure for the much brighter light around the hairline. With the face properly exposed, the area around the back and hairline will become over-exposed. In many cases spot metering will over or underexpose a portion of the scene, so that the point of interest will be correctly exposed.

This mode meters a larger area than spot metering (around 10–15% of the entire frame), and is generally used when very bright or very dark areas on the edges of the frame would otherwise unduly influence the metering. As in spot metering, some cameras can use variable points for readings or use a fixed point in the centre of the viewfinder.

This mode is also called matrix, evaluative, honeycomb, segment metering, or esp (electro selective pattern) metering on some cameras. This metering mode was first introduced by the Nikon FA and was termed Automatic Multi-Pattern metering. On a number of cameras this is the default or standard setting. The camera measures the light intensity in several points in the scene and then combines the results to find the setting for the best exposure. The method of calculation can be different from camera to camera. The actual number of zones used varies widely, from several to over a thousand. The design concept behind multi-zone is to reduce the need to use exposure compensation.[1]

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Clipping is reduced by using a high resolution metering sensor and analyzing each area for washed-out ("blown") highlights or underexposed shadows.[3] Although there are some similarities with multi-zone, matrix, or evaluative metering, this mode uses a high-resolution sensor for detailed detection and gives more weight to reduce clipping.[4]

Now that we have briefly explained what numerical aperture is, we can equate it to f/#. As explained here, f/# is also a measure of how much light can get through a lens. f/# of a simple lens is defined by the following equation, where f is the focal length of the lens and D is the diameter (or more specifically the entrance pupil diameter for more complex lens systems).

Numerical apertureof lens

In order to equate NA and f/#, we can use simple geometric relationships. Figure 3.1 shows a simple lens focusing light rays (blue lines) from infinity to a point. This creates a cone of light that can be described by numerical aperture using the previous equation. The half angle, α, can now be defined by the following equation:

To determine whether lens specifications are compatible, we need to find the resulting numerical aperture from the other three specifications. To do this we will first need to use the equation below to relate the image height h, focal length f and the half field of view Θ. This equation can be derived using simple geometry using the relationships shown in the red triangle in figure 3.2.

In photography, the metering mode refers to the way in which a camera determines exposure. Cameras generally allow the user to select between spot, center-weighted average, or multi-zone metering modes. The different metering modes allow the user to select the most appropriate one for use in a variety of lighting conditions. In complex light situations professional photographers tend to switch to manual mode, rather than depending on a setting determined by the camera.

This is an exact equation relating the NA to the f/#, but it is often convenient to have an approximation for this. When n = 1 (medium is air) and if we use a small angle approximation (sin α ≈ tan α) then:

Another example of the use of spot metering is photographing the moon. Other metering methods will increase overall exposure in an attempt to lighten the dark sky area, resulting in overexposure of the moon. Spot metering gives correct exposure of the moon and underexposes the rest of the scene which was dark already, so the low exposure is not noticeable. Spot metering may also be used for theatre photography, where brightly lit actors appear in a darkened auditorium. Spot metering is a method upon which the Zone System depends.

Numerical apertureof microscope

Many manufacturers keep their exact calculation methods confidential as proprietary information. A number of factors are taken into consideration, including: autofocus point, distance to subject, areas in or out of focus, colours/hues of the scene, and backlighting. Multi-zone tends to bias its exposure towards the autofocus point, thus ensuring that the point of interest has been exposed for properly. A database of thousands of exposures may be pre-stored in the camera, and the processor can use that information to determine what is being photographed.[2]

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The larger the f-number, the smaller the aperture. So how do you know which aperture setting to use? Check out this guide to get familiar with common apertures ...

If the medium is not air, as is common for some microscope objectives, the approximation above can be multiplied by the index of refraction of the medium as shown below.

With spot metering, the camera will measure only a very small area of the scene (1–5% of the viewfinder area). By default this is the centre of the scene. The user can select a different off-centre spot or recompose by moving the camera after metering. Certain models support a mode which allows averaging of multiple spot meter readings, and some support metering of highlight and shadow areas.