An interference is the phenomenon in which two or more beams of light overlap each other on the same point and they are strengthened and weakened each other.
Interference fringes are the bright and dark stripe patterns which are caused by interference.
(An interferometer is an optical device which is configured to create interference fringes through the use of light interference and analyze various pieces of information from such interference fringes.）

Considering that beams of light emitted from one light source overlap (interfere) with each other at a certain point and that the condition at that stage is regarded as wave motion, the explanation can be offered as mentioned below.
The beams of light are strengthened each other when a phase of the two overlapping wave motions is the same (a cycle between the wave crests or troughs is the same or a periodic variation is the same at a given time), whereas they are weakened each other when the phase is inverted (the periodic variation at a given time is out of phase with each other by a half cycle even though the cycle between the wave crests or troughs is the same).
Meanwhile, when the phases of the two overlapping waves differ from each other (the periodic variation at a given time is out of phase with each other even though the cycle between the wave crests or troughs is the same), they are strengthened or weakened each other depending on such difference in phase between them.

The fact that the wave motions are strengthened each other means the amplitude becomes larger (or the wave crest becomes higher) than that prior to the overlapping at that position.

On the other hand, the fact that the wave motions are weakened each other means the amplitude becomes smaller (or the wave crest becomes lower) than that prior to the overlapping at that position. Under the condition that the beams of light are strengthened each other, they become brighter than they were before they were overlapped with each other at that position. By contrast, under the condition that the beams of light are weakened each other, they become darker than they were before they were overlapped with each other at that position.

Now, the following explanation can be given, considering a situation under which the beams of light are overlapped with each other as planes that extend like waves on water surface:
The line along which wave crests range is represented by a solid line; the line along which wave troughs range is indicated by a dashed line; the positions at which wave crests overlap when two waves overlap are marked with ○; the positions at which wave troughs overlap are marked with ●; and the positions at which wave crests overlap with wave troughs are marked with ×.
They are strengthened each other at the positions where the crests overlap (marked with ○) and where the troughs overlap (marked with ●), while as they are weakened each other at the positions where the crests overlap with the troughs (marked with ×), and hence the line along which ○ is connected with ● is a portion where they are strengthened each other, and the line formed by a series of marks × is a portion where they are weakened each other.
The overlapping (interfering) of two waves with each other produces a pattern wherein portions where they are strengthened and weakened each other are created alternately. This pattern will be an interference fringe caused by the interference.

　
Even when beams of light which spread less overlap as planes with each other like a laser beam, interference fringes are also created because the portions where they are strengthened and weakened each other are formed alternately.

　
A distance between interference fringes (an interval at which interference fringes are formed) is determined by a wavelength of a beam of light used and an intersection angle of overlapping beams of light.
Under such conditions as d: Distance between interference fringes, λ: Wavelength of a beam of light used and θ: Intersection angle of overlapping beams of light,
the equation of d = λ/2sin(θ/2) holds.
Based on this equation, as the intersection angle, becomes larger and the wavelength used becomes shorter, the distance between interference fringes, d, is decreased (or becomes shorter).
As an example, when λ equals 0.6328 μm and θ equals 180°, the equation of d = 0.3164　μm holds; and when λ equals 0.6328　μm and θ equals 90°, the equation of d = 0.4475　μm holds.
In the case where 1 mm of the distance between interference fringes is desired, the intersection angle, θ, needs to be 0.036°.

A laser beam is an ideal light beam to cause interference and to create interference fringes.
Because the laser beam (from a laser light source of linear polarized light output) usually has the coherence length of several hundred millimeters (mm), it is used for holography and so on, including interferometer.
In this case, however, interference and interference fringes cannot be generated if a linearly polarized laser beam is not used.
Furthermore, two light beams to be overlapped should be placed in the identical polarization state. In the event that a laser beam of linearly polarized output is divided into polarization components (P and S polarized light beams) by means of a polarization element (such as polarizing beam splitter), the beam needs to be returned to the identical polarization state.

Even if a laser beam of lineally polarized output is used, no interference can be caused even though two laser light sources are used.
In this case, a laser beam emitted from a single laser light source needs to be divided into two laser beams, and these two beams are required to be overlapped again based on a light path difference between them which is within the coherence length of the laser beams.

Although a light path difference between adjacent interference fringes is equal to one wavelength of a beam of light, it becomes equal to 1/2 wavelength as a difference in height on the surface of a sample because a reflected light beam from the sample surface travels to and from the surface. Accordingly, because λ equals 0.6328 μm when the He-Ne laser beam is used, the difference in height on the sample surface which is indicated by adjacent interference fringes will be λ/2 = 1/2 x 0.6328 μm = 0.316 μm. While in general λ/4 or λ/10 and so on are used to express the surface roughness of a mirror, these values are based on evaluation made on observation of Newton ring with a white light beam by means of an optical flat and Newton gauge. The reference wavelength for this evaluation refers to λ = 0.546 μm which is the bright line spectrum of Hg.
The surface of a measurement mirror to which mirror finish is applied generally has a smooth concave-convex-like surface, and its stripe pattern can be observed as shown in the figure below.

　
Although, as a matter of course, the actual surface becomes more complicated to look like contour line of a map, a simple concave-convex surface shows a stripe pattern as shown above. While both of a inclined surface and a wavy surface exhibit a straight-line-like pattern, the entire surface will have the same brightness and darkness in the case of the inclined surface if the surface is oriented vertically with respect to an optical axis. However, in the case of the wavy surface, its stripe does not have one color and the surface will not change to a straight-line-like shape depending on a direction in which it is inclined. Because both the concave and convex surfaces have the same stripe pattern, the other side should be lifted upward and tilted slightly to ascertain whether a surface is concave or convex surface. Then, it should be concluded that if the center of stripe pattern moves to the lifted point, it is the convex surface, and it is the concave surface if the same center moves away from the point. Furthermore, when it is lifted parallelly, it is the convex surface if a ring-shaped stripe pattern starts appearing from the center; and it is the concave surface if the pattern is attracted to the center. For this reason, there are some cases where a judgment as to whether a surface is concave or convex surface is made by moving a mirror back and forth very little when the surface is wavy surface or combined surface of concave and convex surfaces. Although the aforesaid evaluations are made when several stripes exist, the following evaluation is made if there is only one stripe or no stripe:
In other words, in the event that only one color appears if a reference mirror is positioned in parallel with a sample mirror, a straight-line-like stripe pattern appears in the direction of tilt when the sample mirror is tilted slightly. Then, if the number of this stripe is five, the inclined angle, α, at this stage will be as follows, provided that the mirror's size is φ50 mm:
α = Tan-1 (1/2 x 0.6328 x 10-3 x 5)/50≒6.5''.

　
If the surface is distorted only as much as h in the form of concave between A and B, the straight line will be curved slightly. However, the amount of distortion, h, will be （b/(2a））・if the surface has a convex shape in this instance, the center of curve will be provided on the lifted side. Moreover, although what are mentioned above apply to a distortion in the form of A-B line with the inclination toward Y-Y' direction, other stripes enable a distortion relative to other points to be identified. Additionally, a distortion can be seen in the X-X' direction while the surface is inclined in the Y-Y' direction. By inclining it in other directions in the same manner, a state of the entire distortion should be judged, and a value obtained in the worst direction should be the surface roughness.

In the Fresnel holography, both the object beam and reference beam are incident on a photosensitive material from an identical direction to create an optical system that records interference fringes.
If illumination is provided by means of the same light beam as the reference light beam used to photograph a hologram that has recorded, developed and processed interference fringes, a reproduced image (virtual image) appears at the position in the back of hologram where a photographed image was placed.

In the Michelson interferometer, a bundle of light rays which is enlarged by a spatial filter is divided into two portions in its entirety through a beam splitter.
Then, the two beams of light ray which are divided as such travel toward a mirror without being changed at all, following which they are overlapped by the beam splitter after they are reflected.
In the light path beyond this beam splitter, interference fringes are generated at this stage owing to a difference in light paths until the beams reach a screen.
The interference fringes to be obtained will change when the difference in light path between the two beams of light ray becomes equal to 1/2 wavelength of the light source used.

In the Mach-Zehnder interferometer, a bundle of light rays which is enlarged by a spatial filter is transformed into a parallel light beam through a collimating lens.
The, the two beams of light ray which are divided by the first beam splitter travel forward without going to and returning from the light path, following which they are overlapped by the second beam splitter.
When a sample is put in the other light path, an interference fringe is generated which indicates the sample's state.

In the Fizeau interferometer, a bundle of light rays which is enlarged by a spatial filter is transformed into a parallel light beam through a collimating lens.
A beam splitter is located between the spatial filter and the collimating lens.
An interference fringe is produced by a reflected light if a reference flat plane and a sample mirror are put in a bundle of parallel light rays.

The term "schlieren" which is one of the optical terminologies means striae (portions of which index of refraction is nonuniform which are inherent in optical glass, etc.).
In the German language, it means a striate mark or stripe and the like.
The schlieren method expresses a small change in index refraction as a difference between brightness and darkness by making use of refraction of light.
The schlieren optical device uses this schlieren method.

In the schlieren method, an transparent medium (photographic subject) which is optically uneven in terms of dispersion, refraction, etc. is put in an uniform bundle of parallel light beams which is free from irregular brightness and unevenness, and the medium is brought into focus with lens.
Although the brightness is decreased when a knife edge is placed at the lens's focal position to block a beam of light, a light-dark contrast will be increased in the dark condition because the light path is disturbed if there is any uneven portion or air bubble and so on.

The schlieren method can be applied to not only visualization of changes in optical index of refraction of a transparent medium such as glass as well as of changes which occur in gas flow, such as hypersonic gas and shock wave, at a wind tunnel test, etc., but also to the case where a density difference in gas or liquid is visualized for gas injection, combustion, explosion or the like.
This method is characterized by (1) use of a parallel light beam and (2) use of a knife edge.

(1) Use of parallel light beam:
A parallel light beam is disturbed if there is a difference (nonuniformity) in index of refraction of a transparent medium (photographic subject) located inside a beam of parallel light rays and such difference in density of gas. This disturbance is then observed (or "visualized" is used often) as schlieren. Using a parallel light beam in combination with a knife edge allows for an accurate observation of the disturbance.

(2) Use of a knife edge:
While the brightness decreases when a knife edge is placed in position to cut out a light beam (at a lens's focal position) if a parallel light beam is not disturbed, the brightness decreases further if the parallel light beam is disturbed and a disturbance of the light beam is caused toward the knife-edge side, and the brightness increases if the light beam on the opposite side of the knife edge is disturbed.
Also, a light-dark contrast will increase more if the knife edge cuts out the light beam from the direction opposite to the direction in which the index of refraction (density) changes. In a density change wherein air drifts upward that can be seen in a lighter's flame, clothes iron's heat, etc., the brightness and darkness can become clear if the knife edge is used for the top-to-bottom cutting out after the knife edge is placed horizontally. In the event that a density change occurs transversely in supersonic, shock wave or the like, use the knife edge for the cutting out from the direction opposite to the direction in which such change occurs with the knife edge positioned vertically.
What counts for observation (recording) using the schlieren method is③ optical system layout.

(3) Three types of layouts seem to be available as shown below,
from the viewpoint of a relationship with distance (La) between the lens 2 (L2) which collects parallel light beams and the object (Obj), or with the focal length (f2) of the lens 2 (L2).

　
When the distance (La) between the lens 2 and the object is larger than the lens 2's focal length (f2) [La ＞ f2]: Under the condition that La is larger than f2
, a real image is created at the position which is kept apart from L2 by 2, 000 mm (on the side of an observer) when La = 2, 000 mm and f2 = 1,000 mm.
The real image can be observed as it is if a screen is put at such position, whereas it is created at a considerable distance, depending on the focal length (f2) of the lens 2 (L2) used and the object's position. Incidentally, when La equals 1,500 mm and f2 equals 1,000 mm, a real image is created at the position which is away from L2 by 3,000 mm (on the side of an observer).
As La is closer to f2, the real image is created at a further distance and the magnifying power is increased.
Although a recording can be made if a camera is put at the real image's position, there is a case where all the images cannot be recorded because of a magnifying power of the images.
While the lens 3 (L3) is used for the camera recording, such use functions as a synthetic optical system of the lens 2 and lens 3, and therefore not only a layout but also the image's magnifying power must be determined by calculation.
In this situation, because no focus can be placed under the condition that the lens and camera are fixed in position by means of Nikon F mount, C-mount and the like (where a position at which an image is created is predetermined when a lens is mounted in place), some focus adjustment mechanism which utilizes rails (bellows) as seen in close-up photography is required separately.

　
When the distance (La) between the lens 2 and the object is the same as the lens 2's focal length (f2) or smaller than that length (La = f2 or La ＜ f2):
Under the condition that La is equal to f2, an image is created at an infinite distance (without depending on La and f2).
When La equals 500 mm and f2 equals 1,000 mm under the condition that La is smaller than f2, a virtual image is created at the position (on the object side) which is away from L2 by -1,000 mm.
When La ≦ (is equal to or larger than) f2, an image is created at an infinite distance or a virtual image is created, and thus no real image can be created with the lens 2 alone. In this case, use another lens, the lens 3 (focal length: f3), to create a real image of the object (on the observer side).
With the lens 3, the image can be projected onto a screen and recorded with a camera placed in position.
A magnifying power of the image when La equals f2 is determined by a ratio of the focal length of the lens 2 to the lens 3 (magnifying power, m = f3/f2).If both the lens 2 and lens 3 have the same focal length, their magnifying power becomes identical, whereas if the lens 3's focal length is one-half of that of the lens 2, the resultant magnifying power is reduced by half. According to an available space or a required magnifying power, the lens 3's focal length can be selected.

　
Using a single lens where La equals f2, an image can be projected onto a screen, and the image can also be brought into focus under the condition that both the lens and camera are fixed in position by means of Nikon F mount or C-mount and the like.
Using a single lens where La is smaller than f2, an image can be projected onto a screen, and the image can also be brought into focus even if the lens is used under the condition that both the lens and camera are fixed in position by means of Nikon F mount or C-mount and the like, provided that a particular attention is paid to the shortest photographing distance of a camera lens.

Even if the lens 2 is not a condenser lens but a concave mirror, the same conception as that mentioned above can also apply.

As holography-related data, the "technical data of photosensitive materials for holography" and "Chuo Seiki's holography: Revised 5th edition" are contained in the appendix.

■ Technical data of photosensitive materials for holography:
It contains the technical data of various photosensitive materials for holography (spectral absorbance properties and exposure characteristics).Please make use of the data for selecting our photosensitive materials for holography.
PDF data　(about270KB)

■ Chuo Seiki's holography - Revised 5th edition:
It contains the necessary technical data that cover the topics ranging from the basic principles to the photographing and developing methods of holography as well as the formula of developing fluid and liquid bleach. This material particularly instrumental in helping you to use any of our photosensitive materials for holography.
PDF data　(about612KB)

In the Twyman-Green interferometer, a bundle of light rays which is enlarged by a spatial filter is transformed into a parallel light beam through a collimating lens.
Then, the two beams of light ray which are divided by a beam splitter travel toward a mirror as they are, following which they are overlapped by the beam splitter after they are reflected.
In the light path beyond this beam splitter, interference fringes are generated at this stage owing to a difference in light paths until the beams reach a screen.
The interference fringes to be obtained will change when the difference in light path between the two beams of light ray becomes equal to 1/2 wavelength of the light source used.