Beam Manipulation: Prisms Vs. Mirrors

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Beam manipulation: prisms vs. mirrors

Andrew Lynch, Edmund Optics Inc., Barrington, NJ, USA Kai Focke, Edmund Optics GmbH, Karlsruhe, Germany

Designers of beam manipulation and imaging systems often encounter the need to fold their optical layout into a more compact form, or to redirect light to the next component. In either case, the choice inevitably arises between mirrors, or alternatively, prisms. Solutions may often be found either way, but making the best selection up-front could save the designer from potential problems later.

The general concept of using a refl ective optimal for weight sensitive applications, absorption and heat build-up, which could surface to refl ect light needs no explanation. or where material absorption or chro- permanently damage or ultimately even For discussing mirrors and prisms in beam matic aberration could be of concern. A crack the prism. Mirrors are also preferrable steering applications, one mainly just needs prism retrorefl ector would likely be optimal in applications where fl exibility and quick to understand the Law of Refl ection: it where thermal effects may be a concern changes are more important than other essentially shows that the angle of light inci- (more on this later). system parameters. One major disadvan- dent on a plane surface is equal to the angle Both mirrors and prisms can also be used tage to a mirror-based layout, however, is of refl ection (fi gure 1). Combining several to split or combine beams of light, or the need for mounting fi xtures for each refl ective planes with each other yields a simply to “fold” optical systems into physi- mirror. With multiple mirrors and mounts, higher number of potential applications. For cally smaller spaces. Every refl ecting prism positioning issues and alignment complex- example, two plane mirrors oriented at a actually has a mirror-based equivalent. ity can quickly become worrisome. given angle α to each other will refl ect an In theory, these different approaches are incident beam of light by twice that angle, mostly interchangeable methods for bend- Using prisms 2α, as long as the plane of incidence is ing paths of light. In reality, however, the perpendicular to the line of intersection of performance characteristics and benefi ts Instead of using multiple mirrors in a the mirror planes. This can also be seen in of these two approaches can be appreci- number of potentially cumbersome and fi gure 2: The angular sum within the yellow ably different. costly mounting fi xtures, one could often triangle is θ1 + θ2 + (180° - α) = 180°, and Whether to use mirrors or a prism largely simply use a prism. Prisms are solid pieces thus θ1 + θ2 = α. Therefore, a beam defl ec- depends on the complexity and purpose of of glass (sometimes other materials) with tion of 2θ1 + 2θ2 equals 2α. From this, one the layout in question. polished faces that have been worked can see that the special case of two mir- into optically meaningful shapes. Their rors oriented 90° to each other will return Using mirrors effect depends on the position, number, a beam oriented 180° (anti-parallel) to its and angles of faces. Prisms work similarly original direction as shown on the right For many simple layouts, a mirror-based to mirrors in that they are able to redirect hand side in fi gure 2. solution may save cost and reduce the light into different angles or around obsta- By adding a third refl ective surface to cre- weight of a given system (assuming that cles, based on refl ection. As a monolithic ate a right angle “corner” of three plane off-the-shelf mirrors can be used). A mirror component, an appropriately toleranced mirrors, it can be shown that a beam will system might also make sense when sys- prism can often avoid common alignment be returned upon itself no matter what the tem size is not a constraint, e.g. on a large problems that plague a similar mirror- angle or plane of incidence, as long as the bench. Mirrors are favorably used for wave- beam hits all three mirrors successively as length ranges that are strongly absorbed in fi gure 3. Such a confi guration is called by most types of glass. High power laser a corner cube retrorefl ector (fi gure 4) and applications where even partial absorp- is extremely useful in laser-based align- tion may be a concern could be another ment applications. Retrorefl ectors can be strong case for using mirrors rather than found in either mirror or prism form. A prisms. Any bubbles or inclusions in the mirror-based retrorefl ector would likely be glass of a prism could lead to preferential

Figure 2: Two mirrors oriented at angle α will turn a beam by an amount twice that angle. In the special case shown on Figure 1: Angle of Incidence (θi) = Angle of Refl ection (θr) the right hand side, a 90° orientation will turn the beam 180°

Originally published in German in Photonik 3/2009 Photonik international · 2009/2 45

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Figure 3: Three mirrors arranged in a right angle Figure 5: “corner” confi guration will Figure 4: A corner cube retro- A penta prism has two refl ective surfaces oriented at 45°, which return a beam back to its refl ector prism produces a 90° beam deviation regardless of the input angle source (with some offset) from any incident angle as beam in one dimension. This is achieved a prism-based beamsplitter is the cube long as all three mirrors are by adjusting the angle of tilt between beamsplitter, which is composed of two hit successively the two wedge prisms, and is useful right angle prisms cemented together at for making elliptical laser beams circular their hypotenuses. More complex prism- based approach. For example, consider (see fi gure 7). A pair of wedge prisms, based beamsplitter and beam combiner the case of using a penta prism instead referred to as a Risley prism, can also assemblies are often used in certain laser of one or two plane mirrors in order to “steer” a beam anywhere within a circle targeting and laser range-fi nding applica- bend a laser beam by 90° (see fi gure 5). described by the full angle 4θ, where θ tions. A penta prism will yield a resultant beam is the deviation from a single prism (see It is necessary to add a note of caution at 90° with respect to the incident beam, fi gure 8). when using prisms with either convergent in the plane shown, regardless of minor By applying special coatings between or divergent light, or when the entrance alignment errors of the prism or input prisms that are to be cemented together, or exit face of the prism is at an angle to beam. Conversely, it is easy to picture the any number of potential beamsplitter and the incident light. Any of these conditions diffi culty of aligning a mirror (or mirrors) beam combiner assemblies can be created will introduce aberrations (both monochro- at exact angles in order to yield the same that would be very diffi cult to duplicate matic and chromatic). In the case of laser result. Note that any alignment error with effectively with similar specialized plane beam steering, convergent or divergent a mirror is doubled on account of the Law mirror coatings. The simplest version of input light would suffer from spherical of Refl ection. Besides the aforementioned retrorefl ector prism and penta prism, other prisms that d) are commonly used in beam manipulation applications include: the right angle prism, a) the dove prism, the rhomboid prism, and wedge prisms (see fi gure 6). The right angle prism is quite a versatile component. Depending on orientation, a right angle prism can either be used to turn a beam 90° by refl ecting it off of the hypotenuse, or to turn a beam 180° by refl ecting it off of the orthogonal faces, with a predictable amount of beam displacement. In both d) cases, refl ection occurs internally. A dove prism is essentially a right angle prism that is truncated for weight and size concerns. Both the dove and right angle prism can be b) used for beam displacement, by translating it in the plane of incidence, or for beam rotation, by rotating the prism about an axis parallel to the incoming beam. A rhomboid prism is useful for displacing the optical axis without changing the beam direction. c)

Unique features of prisms Prisms can also be used as refractive ele- ments. An individual wedge prism as in fi gure 6 will deviate a laser beam at a Figure 6: a) A right angle prism, b) a set angle, while an anamorphic pair of rhomboid prism, c) a wedge prism, and two wedge prisms can expand a laser d) a dove prism

46 Photonik international · 2009/2 Originally published in German in Photonik 3/2009

Optical Components

It is also possible to design and achieve very high refl ectance mirrors, but they have to be tailored to specifi c wavelengths by using certain specialized dielectric coatings (i.e. “laser mirrors”), and the cost of such mirrors are often in the range of hundreds of dollars. At that point, there is often just a negligible cost difference between pre- mium mirrors and precision prisms or prism pairs that are appropriately antirefl ective coated to minimize refl ection losses at Figure 8: Beam steering in a Risley prism each air-to-glass interface. is accomplished by rotating the wedge prisms independently of each other Figure 7: An anamorphic pair uses two tilted wedge prisms to expand a laser Thermal stability beam in one dimension or change its There are other benefi ts to using prisms ellipticity Literature: rather than mirrors, where applicable. As [1] W.J. Smith, Modern Optical Engineering, McGraw- a uniform piece of glass, a prism is fairly Hill, New York, 2000 aberration, while tilted prism faces would naturally athermalized. In other words, [2] R.E. Hopkins, R. Hanau, Mirror and Prism Sys- likely lead to astigmatism. the entire prism would expand or contract tems, Military Standardization Handbook: Opti- cal Design, MIL-HDBK 141, U.S. Defense Supply with a given homogeneous temperature Agency, Washington, D.C., 1962 Effi ciency change. Such a uniform expansion or contraction is much more unlikely to have A topic that should now be discussed is the a detrimental effect to the optical system Author contact: relative effi ciencies of prisms and mirrors, of which the prism is a part of. Mirrors Andrew Lynch with regard to maximizing the amount of and their mounts made of various metal Applications Engineer light put through a given system. It is desir- components would likely have much more Edmund Optics Ltd able to have refl ections of light inside of a severe reactions to changes in tempera- 101 East Gloucester Pike prism happen as a result of Total Internal ture. Prisms tend to be less affected than Barrington, NJ 08007 Refl ection, or TIR. This occurs when the angle mirrors by other environmental variations USA of incidence θi of a beam traveling from a as well, which is again due to the fact that Tel. +1/856/547-3488 material of higher index (i.e. glass, refractive they are solid blocks of glass rather than Fax +1/856/573-6233 index n1 = 1.5) to a material of lower index individual “exposed” components. eMail: [email protected] (i.e. air, n2 = 1) exceeds the critical angle θc Internet: www.edmundoptics.com required for the light to stay inside the prism, Conclusion rather than refract out of the prism into the Kai Focke air (i.e., θr < 90°). According to Snells Law: Although mirrors certainly have their uses Technical Sales in a variety of systems, especially in opti- Zur Gießerei 19-27 n · sin (θ ) = n · sin(θ ) (Eq. 1) 1 i 2 r cal bench layouts with basic system folds, 76227 Karlsruhe An angle of the refracted beam of θr ≥ 90° many designs switch to using prisms at Germany means that no light is escaping across that the prototype stage and beyond because Tel. +49/721/6273730 interface. Therefore, at θr = 90°, Eq.1 with of the various benefi ts of prisms discussed Fax +49/721/6273750 θi = θc turns into: above. Such a substitution can often result eMail: in a decrease in alignment issues, overall [email protected] θc = arcsin(n2/n1) (Eq. 2) system size, and general maintenance. If Internet: www.edmundoptics.de For a typical glass-to-air interface, this specifi ed correctly, requires θi to be greater than θc ≈ 42°. an increase in accu- TIR is 100% effi cient provided the refl ect- racy and simplicity ing surface is clean and free of defects. could also often Appropriate antirefl ection coatings on the be realized at this entrance and exit faces of the prism would stage. Although ensure that only a negligible amount of the choice between light is lost from unwanted refl ections at using mirrors or each of the air-to-glass interfaces. prisms is applica- If TIR is not met, then a metalized mirror tion-dependent, coating will need to be applied to the having a rough offending prism face to facilitate refl ec- understanding of tion. A downside of a metalized mirror which choice to coating – and standard mirror coatings in make – and why – general – is that there is often a signifi cant may save precious drop in effi ciency. A standard metal mirror design, prototype, coating may not be much more than 90% and maintenance effi cient, for example, with the balance of efforts and costs in the light being scattered or absorbed. the long run.

Originally published in German in Photonik 3/2009 Photonik international · 2009/2 47