Selecting the best prisms for your needs
INTRODUCTION TO OPTICAL PRISMS
Prisms are solid glass optics that are ground and polished into geometrical and optically significant shapes. The angle, position, and number of surfaces help define the type and function. One of the most recognizable uses of prisms, as demonstrated by Sir Isaac Newton, consists of dispersing a beam of white light into its component colors (Figure 1). This application is utilized by refractometer and spectrographic components. Since this initial discovery, prisms have been used in “bending” light within a system, “folding” the system into a smaller space, changing the orientation (also known as handedness or parity) of an image, as well as combining or splitting optical beams with partial reflecting surfaces. These uses are common in applications with telescopes, binoculars, surveying equipment, and a host of others.
A notable characteristic of prisms is their ability to be modeled as a system of plane mirrors in order to simulate the reflection of light within the prism medium. Replacing mirror assemblies is perhaps the most useful application of prisms, since they both bend or fold light and change image parity. Often, multiple mirrors are needed to achieve results similar to a single prism. Therefore, the substitution of one prism in lieu of several mirrors reduces potential alignment errors, increasing accuracy and minimizing the size and complexity of a system.
Figure 1: Dispersion through a Prism
PRISM MANUFACTURING
Before delving into the theory behind prisms, consider their manufacturing process. In order to be used successfully in most applications, prisms must be manufactured with very strict tolerances and accuracies. Due to the variability in shape, size, and, most importantly, the number of surfaces, a large-scale automated process for prism manufacturing is quite infeasible. In addition, most high precision prisms tend to be made in low quantities, meaning an automated process would be unnecessary.
First, a block of glass (known as a “blank”) of a specified grade and glass type is obtained. This block is then ground, or generated, by a metal diamond bonded wheel into a near-finished product. A majority of the glass is removed quickly in this stage resulting in flat, but still coarse surfaces (Figure 2a). At this point, the dimensions of the prism-to-be are very close to the desired specifications. Next is a fine grinding process that removes sub-surface breaks from the surface; this stage is known as smoothening. Scratches left from the first stage are removed in the second stage (Figure 2b). After smoothening, the glass surfaces should appear cloudy and opaque. In both the first two stages, the prism surface must be wet in order to expedite glass removal and prevent overheating of the glass itself.
Figure 2a: Prism Manufacturing Process: Generating Stage
Figure 2b: Prism Manufacturing Process: Smoothening Stage
The third stage involves polishing the prism to the correctly specified surface accuracy. In this stage, the glass is rubbed against a polyurethane polisher wet with “slurry,” an optical polishing compound typically comprised of water mixed with pumice or cerium oxide (Figure 2c). The exact duration of the polishing stage is highly dependent on the surface specifications required. Once polishing is completed, chamfering can begin. In this fourth stage, the edges of the prism are subjected to a spinning diamond plate in order to slightly dull the sharp edges it obtains throughout the aforementioned steps (Figure 2d). After chamfering, the finished prism is cleaned, inspected (via both manual and automated means), and coated with anti-reflection (AR) and/or metallic mirror coatings, if necessary, to further aid in overall transmission and/or reflection. Though the process is much more involved and may require more iterations or operations due to the number of surfaces on a prism, the Generating, Smoothening, Polishing and Chamfering Stages are roughly outlined in Figures 2a - 2d.
Figure 2c: Prism Manufacturing Process: Polishing Stage
Figure 2d: Prism Manufacturing Process: Chamfering Stage
Throughout the manufacturing of a prism, it is necessary to continually adjust and secure each surface being worked on. Securing a prism in place involves one of two methods: blocking and contacting. Blocking entails arranging the prism in a metal tool with hot wax. Contacting, on the other hand, is an optical bonding process done at room temperature where two clean glass surfaces are fastened together simply through their Van Der Waals interaction. Contacting is utilized if high precision tolerances are required because it does not require additional adjustments to be made during the Generating, Smoothening, or Polishing Stages to account for the wax thickness between the prism surface and the contact block.
During every stage of the prism manufacturing process, from generating to blocking and contacting, a skilled optician is required to manually inspect and adjust the prism surfaces being worked on. As a result, it is extremely labor intensive and requires experience and skill in order to complete. The entire process often requires a significant amount of time, work, and concentration.
THEORY: LIGHT AND REFRACTION
Understanding how a prism works is key to deciding which type of prism fits best for a specific application. In order to do so, it is important to first understand how light interacts with an optical surface. This interaction is described by Snell’s Law of Refraction:
Where n1 is the index of the incident medium, θ1 is the angle of the incident ray, n2 is the index of the refracted/reflected medium, and θ2 is the angle of the refracted/reflected ray. Snell’s Law describes the relationship between the angles of incidence and transmission when a ray travels between multiple media (Figure 3).
Figure 3: Snell’s Law and Total Internal Reflection
A prism is notable for its ability to reflect the ray path without the need for a special coating, such as that required when using a mirror. This is achieved through a phenomenon known as total internal reflection (TIR). TIR occurs when the incident angle (angle of the incident ray measured from normal) is higher than the critical angle θc:
Where n1 is the index of refraction for the medium where the ray originates, and n2 is the index of refraction for the medium where the ray exits. It is important to note that TIR only occurs when light travels from a high index medium to a low index medium.
At the critical angle, the angle of refraction is equal to 90°. Referencing Figure 3, notice that TIR occurs only if θ exceeds the critical angle. If the angle is below the critical angle, then transmission will occur along with reflection as given by Snell’s Law. If a prism face does not meet TIR specifications for the desired angle(s), then a reflective coating must be used. This is why some applications require coated versions of a prism that would otherwise work well uncoated in another application.
THEORY: IMAGE HANDEDNESS/PARITY
A significant aspect of imaging through a prism is image handedness (parity), otherwise referred to as the orientation of the image. This is introduced every time the ray path hits a plane mirror, any flat reflective surface, or a prism surface at an angle that produces TIR. There are two types of handedness: right and left. Right handedness (Figure 4) describes the case where an image undergoes an even number of reflections, resulting in the ability to read it clearly (assuming the image is text) in at least one position. Left handedness (Figure 5) describes the case where the image undergoes an odd number of reflections, leading to an irregularity in the position of the image that is comparable to what one sees in a mirror.
In addition to parity, there are three types of image change (Figure 6). An inversion is an image-flip over a horizontal axis, whereas a reversion is an image-flip over a vertical axis. When both are done at the same time, an image rotation of 180° occurs and there is no change in parity. Another way to think of parity is defining it as being determined by looking back against the propagation direction towards either the object or image in its optical space (Figure 7).
When using a prism, consider the following four points:
1. Image handedness changes every time an image is reflected.
2. Any point along the plane of the reflecting surface is equidistant
from the object and its image.
3. Snell’s law can be applied to all surfaces.
4. When testing for image handedness/parity, it is best to use a
non-symmetrical letter such as R, F, or Q. Avoid using letters like
X, O, A, etc.
Figure 4: Right Handedness or Even Parity
Figure 5: Left Handedness or Odd Parity
Figure 6: Inversion (Top), Reversion (Middle), Rotation (Bottom)
Figure 7: How Parity is Determined
TYPES OF PRISMS
There are four main types of prisms: dispersion prisms, deviation (or reflection) prisms, rotation prisms, and displacement prisms. Deviation, displacement, and rotation prisms are common in imaging applications; dispersion prisms are strictly made for dispersing light, therefore not suitable for any application requiring quality images.
Dispersion Prisms
Prism dispersion is dependent upon the geometry of the prism and its index dispersion curve, based on the wavelength and index of refraction of the prism substrate. The angle of minimum deviation dictates the smallest angle between the incident ray and the transmitted rays (Figure 8). The green wavelength of light is deviated more than red, and blue more than both red and green; red is commonly defined as 656.3 nm, green as 587.6 nm, and blue as 486.1 nm.
Deviation, Rotation, and Displacement Prisms
Prisms that deviate the ray path, rotate the image, or simply displace the image from its original axis are helpful in many imaging systems. Ray deviations are usually done at angles of 45°, 60°, 90°, and 180°. This helps to condense system size or adjust the ray path without affecting the rest of the system setup. Rotation prisms, such as dove prisms, are used to rotate an image after it is inverted. Displacement prisms maintain the direction of the ray path, yet adjust its relation to the normal.
Figure 8: Dispersion through a Prism
PRISM SELECTION GUIDE
To aid in selecting the best prisms for specific applications, consider the following selection guide of the most commonly used in the optics, imaging, and photonics industries (click to open in a new window).
OPTICAL PRISM APPLICATION EXAMPLES
The angle, position, and number of surfaces of a prism help define the type and function. To understand how the most popular prisms work and how each can best be used in light reflection and refraction applications, consider right angle prisms, roof prisms, and combination prisms.
Right angle prism
By far the most commonly used prism is the 45° - 90° - 45° prism, known popularly as the right angle prism. It can be used in many ways to achieve different results pertaining to image parity or deviation and is named so for the angles on its triangular faces. The most common application of the 45° - 90° - 45° prism is to treat it as a right angle prism, which has only a single reflection that deviates the incident ray by 90°. The produced image will then become left-handed, but depending upon the position of the prism, can be inverted or reverted (Figure 9).
Using the hypotenuse face of the prism rather than the leg faces allows for another configuration known as the porro prism. This produces a right-handed image since two reflections occur. The ray’s direction is reversed when using a porro prism since the object enters and the image exits the same face. The position of the prism determines whether a rotation or just a deviation occurs (Figure 10).
Lastly, a 45° - 90° - 45° prism can also be used as a dove prism. A dove prism rotates the image 180°, but since only one reflection occurs, it will become either reverted or inverted depending on the position of the prism (Figure 11).
Figure 9: 45° - 90° - 45° as a Right Angle Prism Showing Inversion (Left) and Reversion (Right)
Figure 10: Fixed 180° Rotation with a Porro System
Figure 11: 180° Rotation with a Pechan-Roof Prism
Roof prism
A prism roof consists of two reflecting surfaces located 90° from each other. It is equivalent in function when compared to any other reflecting surface, except handedness does not change. A good example of this is the amici (roof) prism, which is basically a right angle prism with a roof. Under this configuration, a deviation of 90° still occurs, but without changing parity. A roof prism is often used in conjunction with other prisms in order to achieve the desired parity.
Combination prism
Many combination prisms are possible with slight adjustments to the orientation and/or coating applied to the surfaces of the individual prisms used. Ultimately, the application dictates the type of combination necessary. Consider the most wellknown combination prisms: porro system, Pechan (roof) prism, and beamsplitters.
A porro prism is often used in combination with itself to create a porro system (Figure 12) with a total of four reflections. Due to its ability to produce an upside down image rotated 180° from the original while maintaining right-handedness, this type of image erection prism is extremely useful for binocular and telescope applications. It is important to keep in mind that the ray path does become displaced, a fact that must be taken into account when adjusting the rest of the optical components used with a porro system, such as an objective lens and eyepiece for binoculars.
Another type of image erection prism is the Pechan (roof) prism (Figure 13) comprised of a Schmidt prism and a half-penta prism. It carries six total reflections and a small air gap to allow for TIR inside the prism system. The even number of reflections enables the image to stay right-handed. No displacement is produced along the object’s axis if aligned precisely, though the image is inverted.
Lastly, but possibly the most recognizable combination prism, is a cube beamsplitter (Figure 14). Unlike a plate beamspitter (often a plano-window with dielectric and anti-reflection (AR) coatings), a cube beamsplitter is comprised of two right angle prisms. Typically, the two prisms are adhered together, but optical contacted beamsplitters exist as well. In order to “split” the incident beam, a dielectric coating is applied to the hypotenuse of one of the right angle prisms. This coating reflects a portion of the beam in one direction, and allows the other to be transmitted through the entire cube. The type of coating determines whether this split is 50/50, 30/70, or 70/30, as well as the specific wavelengths and/or polarizations that are transmitted or reflected. As a result of the precise alignment required by a skilled optician to adhere or contact the two hypotenuses together, it is better to purchase a complete beamsplitter assembly rather than try to use two identical right angle prisms.
Figure 12: Fixed 180° Rotation with a Porro System
Figure 13: 180° Rotation with a Pechan-Roof Prism
Figure 14: Cube Beamsplitter
Edmund Optics® manufactures prisms in a range of geometries for simple dispersion to complex, multi optical element applications. Understanding the optical theories behind each specific geometry helps one select the best prism or combination of prisms for any application.
