Depth of fieldvsdepth offocusmicroscope

As a numerical example, let’s look at the case of the output from a Newport R-31005 HeNe laser focused to a spot using a KPX043 Plano-Convex Lens. This Hene laser has a beam diameter of 0.63 mm and a divergence of 1.3 mrad. Note that these are beam diameter and full divergence, so in the notation of our figure, y1 = 0.315 mm and θ1 = 0.65 mrad. The KPX043 lens has a focal length of 25.4 mm. Thus, at the focused spot, we have a radius θ1f = 16.5 µm. So, the diameter of the spot will be 33 µm.

The magnification depends on the focal length and the subject distance, and sometimes it can be difficult to estimate. When the magnification is small, the formula simplifies to

Resolutionmicroscope

For minimal aberrations, it is best to use a plano-concave lens for the negative lens and a plano-convex lens for the positive lens with the plano surfaces facing each other. To further reduce aberrations, only the central portion of the lens should be illuminated, so choosing oversized lenses is often a good idea. This style of beam expander is called Galilean. Two positive lenses can also be used in a Keplerian beam expander design, but this configuration is longer than the Galilean design.

Another common application is the collimation of light from a very small source, as shown in Figure 2. The problem is often stated in terms of collimating the output from a “point source.” Unfortunately, nothing is ever a true point source and the size of the source must be included in any calculation. In figure 6, the point source has a radius of y1 and has a maximum ray of angle θ1. If we collimate the output from this source using a lens with focal length f, then the result will be a beam with a radius y2 = θ1f and divergence angle θ2 = y1/f. Note that, no matter what lens is used, the beam radius and beam divergence have a reciprocal relation. For example, to improve the collimation by a factor of two, you need to increase the beam diameter by a factor of two.

The simple formula is often used as a guideline, as it is much easier to calculate, and in many cases, the difference from the exact formula is insignificant. Moreover, the simple formula will always err on the conservative side (i.e., depth of focus will always be greater than calculated).

Field ofviewmicroscopedefinition

Following historical convention, the circle of confusion is sometimes taken as the lens focal length divided by 1000 (with the result in same units as the focal length);[2][3] this formula makes most sense in the case of normal lens (as opposed to wide-angle or telephoto), where the focal length is a representation of the format size. This practice is now deprecated; it is more common to base the circle of confusion on the format size (for example, the diagonal divided by 1000 or 1500).[3]

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This application is one that will be approached as an imaging problem as opposed to the focusing and collimation problems of the previous applications. An example might be a situation where a fluorescing sample must be imaged with a CCD camera. The geometry of the application is shown in Figure 4.  An extended source with a radius of y1 is located at a distance s1 from a lens of focal length f. The figure shows a ray incident upon the lens at a radius of R. We can take this radius R to be the maximal allowed ray, or clear aperture, of the lens.

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Depth of field microscopedefinition quizlet

While depth of field is generally measured in macroscopic units such as meters and feet, depth of focus is typically measured in microscopic units such as fractions of a millimeter or thousandths of an inch. In optometry depth of focus is usually measured in dioptres.

where t is the total depth of focus, N is the lens f-number, c is the circle of confusion, v is the image distance, and f is the lens focal length. In most cases, the image distance (not to be confused with subject distance) is not easily determined; the depth of focus can also be given in terms of magnification m:

is reduced from the original divergence by a factor that is equal to the ratio of the focal lengths |-f1|/f2. So, to expand a laser beam by a factor of five we would select two lenses whose focal lengths differ by a factor of five, and the divergence angle of the expanded beam would be 1/5th the original divergence angle.

In small-format cameras, the smaller circle of confusion limit yields a proportionately smaller depth of focus. In motion-picture cameras, different lens mount and camera gate combinations have exact flange focal distance measurements to which lenses are calibrated.

What isthe focal distanceofamicroscope

Depth of field microscopeformula

Depth of focus is a lens optics concept that measures the tolerance of placement of the image plane (the film plane in a camera) in relation to the lens. In a camera, depth of focus indicates the tolerance of the film's displacement within the camera and is therefore sometimes referred to as "lens-to-film tolerance".

Since a common application is the collimation of the output from an Optical Fiber, let’s use that for our numerical example. The Newport F-MBB fiber has a core diameter of 200 µm and a numerical aperture (NA) of 0.37. The radius y1 of our source is then 100 µm. NA is defined as sine of the half-angle accepted by the fiber, which is approximate to the half-angle, so θ1 ≈ 0.37 rad. If we again use the KPX043 , 25.4 mm focal length lens to collimate the output, we will have a beam with a radius of 9.4 mm and a half-angle divergence of 4 mrad. We are locked into a particular relation between the size and divergence of the beam. If we want a smaller beam, we must settle for a larger divergence. If we want the beam to remain collimated over a large distance, then we must accept a larger beam diameter in order to achieve this.

The same factors that determine depth of field also determine depth of focus, but these factors can have different effects than they have in depth of field. Both depth of field and depth of focus increase with smaller apertures. For distant subjects (beyond macro range), depth of focus is relatively insensitive to focal length and subject distance, for a fixed f-number. In the macro region, depth of focus increases with longer focal length or closer subject distance, while depth of field decreases.

As a first example, we look at a common application, the focusing of a laser beam to a small spot. The situation is shown in Figure 1. Here we have a laser beam, with radius y1 and divergence θ1 that is focused by a lens of focal length f. From the figure, we have θ2 = y1/f. The optical invariant then tells us that we must have y2 = θ1f, because the product of radius and divergence angle must be constant.

Whathappens to thedepth of fieldas total magnification decreases

Depth of field

As an example, consider a Newport R-31005 HeNe Laser with beam diameter 0.63 mm and a divergence of 1.3 mrad. Note that these are beam diameter and full divergence, so in the notation of our figure, y1 = 0.315 mm and θ1 = 0.65 mrad. To expand this beam ten times while reducing the divergence by a factor of ten, we could select a plano-concave lens KPC043 with f1 = -25 mm and a plano-convex lens KPX109 with f2 = 250 mm. Since real lenses differ in some degree from thin lenses, the spacing between the pair of lenses is actually the sum of the back focal lengths BFL1 + BFL2 = -26.64 mm + 247.61 mm = 220.97 mm. The expanded beam diameter

In astronomy, the depth of focus Δ f {\displaystyle \Delta f} is the amount of defocus that introduces a ± λ / 4 {\displaystyle \pm \lambda /4} wavefront error. It can be calculated as[4][5]

This is a fundamental limitation on the minimum size of the focused spot in this application. We have already assumed a perfect, aberration-free lens. No improvement of the lens can yield any improvement in the spot size. The only way to make the spot size smaller is to use a lens of shorter focal length or expand the beam. If this is not possible because of a limitation in the geometry of the optical system, then this spot size is the smallest that could be achieved. In addition, diffraction may limit the spot to an even larger size (see Gaussian Beam Optics), but we are ignoring wave optics and only considering ray optics here.

The phrase depth of focus is sometimes erroneously used to refer to depth of field (DOF), which is the distance from the lens in acceptable focus, whereas the true meaning of depth of focus refers to the zone behind the lens wherein the film plane or sensor is placed to produce an in-focus image. Depth of field depends on the focus distance, while depth of focus does not.

The choice to place gels or other filters behind the lens becomes a much more critical decision when dealing with smaller formats. Placement of items behind the lens will alter the optics pathway, shifting the focal plane. Therefore, often this insertion must be done in concert with stopping down the lens in order to compensate enough to make any shift negligible given a greater depth of focus. It is often advised in 35 mm motion-picture filmmaking not to use filters behind the lens if the lens is wider than 25 mm.

where f/2R = f/D is the f-number, f/#, of the lens. In order to make the image size smaller, we could make f/# smaller, but we are limited to f/# = 1 or so. That leaves us with the choice of decreasing R (smaller lens or aperture stop in front of the lens) or increasing s1. However, if we do either of those, it will restrict the light gathered by the lens. If we either decrease R by a factor of two or increase s1 by a factor of two, it would decrease the total light focused at s2 by a factor of four due to the restriction of the solid angle subtended by the lens.

If s1 is large, then s2 will be close to f, from our Gaussian lens equation, so for the purposes of approximation we can take θ2 ~ R/f. Then from the optical invariant, we have

It is often desirable to expand a laser beam. At least two lenses are necessary to accomplish this. In Figure 3, a laser beam of radius y1 and divergence θ1 is expanded by a negative lens with focal length −f1. From Applications 1 and 2 we know θ2 = y1/|−f1|, and the optical invariant tells us that the radius of the virtual image formed by this lens is y2 = θ1|−f1|. This image is at the focal point of the lens, s2 = −f1, because a well-collimated laser yields s1 ~ ∞, so from the Gaussian lens equation s2 = f. Adding a second lens with a positive focal length f2 and separating the two lenses by the sum of the two focal lengths −f1 +f2, results in a beam with a radius y3 = θ2f2 and divergence angle θ3 = y2/f2.

Depth of focus can have two slightly different meanings. The first is the distance over which the image plane can be displaced while a single object plane remains in acceptably sharp focus;[1][2][clarify] the second is the image-side conjugate of depth of field.[2][clarify] With the first meaning, the depth of focus is symmetrical about the image plane; with the second, the depth of focus is slightly greater on the far side of the image plane.