where λ0 is the vacuum wavelength of the light, and D is the diameter of the beam at its narrowest spot, measured between the 1/e2 irradiance points ("Full width at e−2 maximum"). Note that this means that a laser beam that is focused to a small spot will spread out quickly as it moves away from the focus, while a large-diameter laser beam can stay roughly the same size over a very long distance.

Batteries are chemical devices that depend on chemical reactions to supply electricity. Those chemical reactions are affected by temperature. When batteries get very cold, their voltage drops rapidly. A battery that will power your camera for hundreds of shots at room temperature might only manage a few dozen frames in sub-freezing weather. The good news is that just warming the battery up restores some of its energy. If shooting in cold weather, carry plenty of spare batteries. Keep them warm inside your clothing. Swap the batteries in your camera and the warm batteries inside your clothes often.

Although 0°F is a little extreme, moving from room temperature to outside where the temperature is just below freezing doesn't seem to permanently harm cameras and lenses. What it does do is affect the battery that powers the camera (more on that in a bit). When ideal optical performance is required in cold weather, such as for astrophotography, allowing all of the optical components to stabilize at the ambient temperature before starting to shoot will avoid temporary minor optical issues due to different parts of the lens/camera cooling at different rates.

Pupilaperture

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The most common cause of condensation on camera gear is caused by moving a cold camera and/or lens into a warm, humid environment. If the temperature of the camera or lens is below the dew point of the surrounding air, water droplets will condense on the cooler surfaces. This should be avoided as much as possible.

but θ is defined differently. Laser beams typically do not have sharp edges like the cone of light that passes through the aperture of a lens does. Instead, the irradiance falls off gradually away from the center of the beam. It is very common for the beam to have a Gaussian profile. Laser physicists typically choose to make θ the divergence of the beam: the far-field angle between the propagation direction and the distance from the beam axis for which the irradiance drops to 1/e2 times the wavefront total irradiance. The NA of a Gaussian laser beam is then related to its minimum spot size by

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I live in South Dakota. So, I can go from 75°F (24°C) with moderate humidity (indoors) to 0°F (-18°C) and dry just by stepping outside. Can this damage my lenses?

Limit the number and frequency of extreme environment changes. For instance, rather than bringing your equipment indoors for only a short time before returning outside, keep your equipment in a locker outside.

F-stops

In laser physics, the numerical aperture is defined slightly differently. Laser beams spread out as they propagate, but slowly. Far away from the narrowest part of the beam, the spread is roughly linear with distance—the laser beam forms a cone of light in the "far field". The same relation gives the NA,

A similar thing will happen when you go back inside from the freezing cold, if you have been outside for a while, the dew will occur on the outside of your equipment (notice the fogging of the glass in its outside). This is due to the fact that the low temperature of your equipment is lowering the temperature of the air surrounding it below its dew point. Inside the lens the outside air will raise its temperature but won’t generate any dew because it won’t become saturated.

f-stop是什么

In optical design, the finite distance between the object and the lens must often be considered. In these cases, the working f-number is used instead. The working f-number is defined by making the approximate relation above exact:

Moving from warm to cold environments is usually a lot easier on camera gear, in terms of long term health, than the opposite. The primary culprit is humidity.

When a light ray is incident from a medium of refractive index n to the core of index n1, Snell's law at medium-core interface gives

Multimode optical fiber will only propagate light that enters the fiber within a certain cone, known as the acceptance cone of the fiber. The half-angle of this cone is called the acceptance angle, θmax. For step-index multimode fiber, the acceptance angle is determined only by the indices of refraction:

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Numerical aperture

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Changing environments, especially those that are as extreme the ones you describe, can damage your equipment for reasons you've already described within your question.

This approximation holds when the numerical aperture is small. The f-number describes the light-gathering ability of the lens in the case where the marginal ray before (or after) the lens is collimated. This case is commonly encountered in photography, where objects being photographed are often far from the camera.

In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. The exact definition of the term varies slightly between different areas of optics.

Numerical Aperturecalculator

Consider using weather-resistant cameras and lenses that are designed to work in extreme environments. Consider using a "tough" compact camera.

Fiber NA

But on the other hand, condensation inside the lenses could be a problem due to the electronic that most modern lenses have and fungus proliferation.

Your lens and camera do not go from 75F to 0F immediately due to the thermal inertia of the lens components and because air, in itself, is not a very good thermal conductor.

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I've lived in Canada for a long time now. And my Nikon lenses have always been fine going from a comfy 25 degrees to minus 40 in a matter of minutes. Apart from some lens misting which I need to wipe sometimes, they've been impeccable.

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where n1 is the refractive index along the central axis of the fiber. Note that when this definition is used, the connection between the NA and the acceptance angle of the fiber becomes only an approximation. In particular, manufacturers often quote "NA" for single-mode fiber based on this formula, even though the acceptance angle for single-mode fiber is quite different and cannot be determined from the indices of refraction alone.

Keep your equipment in an insulated enclosure when changing environments so they can acclimate gradually. The more extreme the temperature change, the more time you should allow for acclimation. This applies to blistering heat as well as to freezing temperatures.

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where n is the index of refraction of the medium in which the lens is working (1.0 for air, 1.33 for pure water, and up to 1.56 for oils), and θ is the half-angle of the maximum cone of light that can enter or exit the lens. In general, this is the angle of the real marginal ray in the system. The angular aperture of the lens is approximately twice this value (within the paraxial approximation). The NA is generally measured with respect to a particular object or image point and will vary as that point is moved.

When materials are subjected to sudden temperature changes they can tolerate the change or can be irreversibly damaged. It all depends on the materials involved, the temperature extremes involved, and just how rapid the change is. Take any lens element heated to something like 300-400°F and drop it into a bucket of ice water and it will most likely crack. That doesn't mean walking out of your 75°F house into 0°F winter will have the same effect. In fact, it almost certainly will not.

numericalaperture中文

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In most areas of optics, and especially in microscopy, the numerical aperture of an optical system such as an objective lens is defined by

And if it can cause damage, then what parameters should I stay within to prevent damage (duration of exposure, temperature, humidity, etc.)? And does it make a difference if the lens housing is plastic or metal?

I especially want to know about damage to its optical performance, due to crazing or changes in alignment, or anything else - such as condensation leading to fungus. And I'm including damage to the lens coating. But I'm also curious about other damage. For example, if it shifts the housing clearance and allows more dust to get in, which could impact the image quality.

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Moreover, pro-lens manufacturers use materials that have a very low coefficients of expansion. If I were you I would not worry about sudden contractions or expansion, because they don’t happen and since they don’t happen and the very low coefficient of expansion of the different materials won’t lead to misalignment in pro-lenses. But if you wish you can let the low temperature settle to all components of the lens, which means waiting for a long while as they reduce their temperature to 0F, if you think you need critical accuracy.

In microscopy, NA is important because it indicates the resolving power of a lens. The size of the finest detail that can be resolved is proportional to λ/NA, where λ is the wavelength of the light. A lens with a larger numerical aperture will be able to visualize finer details than a lens with a smaller numerical aperture. Lenses with larger numerical apertures also collect more light and will generally provide a brighter image.

Numerical aperture is not typically used in photography. Instead, the angular acceptance of a lens is expressed by the f-number, f/#, which for a thin lens imaging an object at infinity is given by

But on the other hand your climate must already be very dry (relative and absolute humidity) during the cold season and I don’t think you are increasing the absolute humidity of your “house” by much. If you were increasing the absolute humidity by a lot, you should get a dehumidifier for your equipment closet to avoid the physical phenomena explained before.

The easiest way to avoid condensation is to always put the camera/lens into a sealed bag before moving it from a cold to warm environment. The cold air sealed into the bag will contain less moisture than the warm air inside buildings. Leave the bag closed until the contents have warmed to room temperature. Any condensation that forms will do so on the exterior of the bag.

In multimode fibers, the term equilibrium numerical aperture is sometimes used. This refers to the numerical aperture with respect to the extreme exit angle of a ray emerging from a fiber in which equilibrium mode distribution has been established.

If the lens isn’t airtight, when you move it form a place where it has stayed for a long while that has warm temperature and a high absolute humidity to a place with a much lower temperature and lower absolute humidity, this will be the physic phenomena that'll occur:

This has the same form as the numerical aperture in other optical systems, so it has become common to define the NA of any type of fiber to be