JML Optical

Introduction to Mirrors

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Mirrors often play an important role in the design of optical systems. Flat mirrors serve to fold optical paths into tight-fitting product envelopes. Curved mirrors form images with performance comparable to that of single element lenses. Mirrors can also be used as filters to remove unwanted wavelengths from a beam of light, and to form the essential part of a laser’s feedback mechanism known as “resonant cavity.” They reflect light that has escaped from the amplifying medium and return it for reamplification. 

In some imaging applications mirrors achieve levels of performance that surpass lenses. Sir Isaac Newton preferred mirrors to lenses when he built his telescope because mirrors do not induce chromatic aberrations in their images. A mirror’s reflective coating will focus every color in the same place, whereas a simple or even well-corrected compound lens will suffer from some chromatic aberration.

Surface contour and reflectivity are two basic operational characteristics of a mirror. Surface contour determines image-forming properties while reflectivity determines image brightness and color. Mirrors may be manufactured with any number of surface contours. Most mirrors have flat, spherical, parabolic or elliptical reflecting surfaces.  The reflectivity of a mirror depends upon the material of its reflecting surface. In the past, engineers used gold and silver to make mirrors. Initially, they made solid castings of these expensive metals. In later years, they plated less expensive castings with bright gold or silver layers. At the turn of the century, silver and aluminum were sputtered onto glass substrates.

Since 1930, techniques involving vacuum deposition have been responsible for the development of highly reflective aluminum coatings and non-metallic coatings known as “dielectrics.” The reflectivity of a dielectric reflector can be considerably greater than that of a metallic reflector.

Choosing a Mirror

A designer must specify three characteristics of a mirror:

1. Type of reflective coating (material and reflectivity)

2. Contour of reflecting surface

3. Thin mirror attributes (clear aperture, focal length and f-number) 

Wavelength, geometry of application and required image quality influence these decisions.

Type of Reflective Coating

Metal coatings are usually inexpensive and exhibit reflectivity of 75% to 99% over a wide range of wavelengths. They also are usually insensitive to angular alignment. Many metal coatings are soft and oxidize easily and therefore require protective overcoats such as SiO2 or MgF2 to improve their durability.  Overcoats sometimes increase reflectivity by several percentage points.

Dielectric coatings can be grouped into two classes: broadband and narrowband. The higher cost associated with these coatings is offset by their durability (no protective overcoats are necessary) and higher reflectivity.

Broadband coatings handle a wide range of wavelengths with reflectivities of about 99%. They must be specified for a certain angular alignment because reflectivity is a function of angle of incidence. In other words, reflectivity changes as the angle of incidence changes.

Narrowband dielectric coatings typically achieve reflectivities of about 99%. Special designs can achieve 99.9%. The term “narrowband” is derived from the fact that this type of coating reflects only a narrow range of wavelengths. The location of the range, or “band,” can be adjusted to fall anywhere within the spectrum by modifying the coating design. Like their broadband counterparts, narrowband coatings are sensitive to angular alignment.

A laser mirror should also be specified in terms of its resistance to damage when it is used to reflect a high-power laser beam. Special dielectric coatings have been designed to withstand extremely high-power densities. Sometimes, solid metal mirrors must be used for their superior resistance to thermal stress.

Contour of Reflecting Surface

Mirrors can be either flat or curved. Flat mirrors do not form images; hence, they are used to fold optical paths without altering the nature of the image.  Curved mirrors, which can form an image, are manufactured in a variety of contours because certain contours produce perfect images when they are employed in specific, ideal geometries.

Flat: Since a flat reflecting surface has no optical power, the only effect flat mirrors have is image inversion.  Flat mirrors also serve to steer or deflect laser beams.

Spherical: A concave spherical mirror will perfectly image a point back upon itself when it is located at the surface’s center of curvature. This feature is used in condenser systems to approximately double the brightness of a source.

Parabolic: A parabolic mirror will perfectly collimate a point source of light located at its focus.  Flashlights are designed with parabolic reflectors to create their beams. Conversely, a parabolic surface will perfectly focus an incoming collimated beam that is parallel to its optical axis.  Parabolic mirrors are used in some telescope designs, laser beam focusing devices and solar collectors.

Elliptical: An elliptical mirror will perfectly image a point located at one of its foci to the other focus. In other words, spherical wavefronts that emanate from one focus of an ellipse will experience perfect convergence at the other focus.

Thin Mirror Attributes (clear aperture, focal length and f-number)

When a designer first sketches an optical system, he or she chooses the thin mirror attributes of the mirrors according to the basic requirements of the application. Thin mirror attributes are analogous to thin lens attributes, i.e., focal length, diameter and f-number.  These attributes define the ideal performance characteristics of a mirror including resolution, magnification, distance from object to image and image brightness.

When a designer first sketches an optical system, he or she chooses the thin mirror attributes of the mirrors according to the basic requirements of the application. Thin mirror attributes are analogous to thin lens attributes, i.e., focal length, diameter and f-number.  These attributes define the ideal performance characteristics of a mirror including resolution, magnification, distance from object to image and image brightness.

Flat Mirrors

Flat mirrors do not form images. The image viewed by an observer when peering into a flat mirror is formed by his or her own eye. The mirror serves only to change the path of the optical system. Flat mirrors often are used to fold a large, cumbersome system so that it fits within the envelope of a small product. The flat mirror will not alter the nature of the image; a curved surface, however, can change the fundamental imaging characteristics of a system.

Designers also employ mirrors to invert images left to right or up and down. Reflecting prisms may also be used (see Prisms). This unique capability to invert an image cannot be imitated with any physical transformation other than reflection. For example, an inverted image cannot be created with rotational transformations. To help demonstrate inversion by reflection, visualize two pencils perpendicular to each other, as shown in Figure 1. Pencil A lies within the plane of incidence; therefore, it is inverted upon reflection. Pencil B lies perpendicular to the plane of incidence and its orientation is unchanged by reflection.

Figure 1

In cases where the object is neither parallel nor perpendicular to the plane of incidence, it is rotated through an angle that is between 180 and 0 degrees (see Figure 2).  Although the most common application for flat mirrors is to fold an optical path or to invert an image, there are other applications in which flat mirrors are essential to the

Figure 2

basic system operation. For instance, some interferometers use a flat mirror to direct a reference beam back toward the probing beam for the creation of interference fringes. In some telescope designs flat mirrors direct the image away from the primary light path for unobstructed viewing with the eye or with a camera. In many laser scanners and printers a rotating flat mirror creates the scanning motion of the laser beam.

Flat mirrors come in a variety of shapes: round, rectangular and elliptical. Customers specify shape to conform to the mechanical mounting or aesthetic requirements and to achieve cost savings in large production runs by eliminating waste caused by unnecessary corners or surface area. Pyrex® is the most common substrate for mirrors because it is stable and inexpensive. Problems with homogeneity of Pyrex are avoided by using it for only front surface mirrors; the reflective coating is deposited on top of the substrate and no light propagates through the glass.

In recent years tools involving very hot beams of infrared radiation have become common. An example is a laser welder. Metal substrates are used for mirrors in these environments because their high coefficients of thermal conductivity can be used to stabilize the temperature at the reflective surface.

Spherical Concave

The optical power of a concave mirror is positive, like that of a convex refractive surface. Like a singlet lens, a concave mirror can produce a magnified or reduced inverted image.

An important application can be found in condensing systems. When the light-emitting filament of a bulb is placed near the center of curvature of a spherical, concave mirror, the reflecting surface creates a well-corrected image of the filament. That image is located in the same plane, but slightly displaced from the filament itself. Thus, the apparent brightness of the source is doubled (Figure 3).

Figure 3

Some projection lamps contain a spherical reflector inside the glass bulb. This reflector light would have been lost to the projector’s housing; instead, it is collected and sent back to its point of origin where it can be collected by the condensing lenses. In fact, filaments of these lamps are designed with an open geometry to minimize blocking of the retro-reflected light.

Indicator light sockets will often employ a spherical reflector to maximize apparent brightness for an observer at any viewing angle. Manufacturers of LEDs often build the reflector into the electronic package. Another application for spherical concave mirrors is spectrometry. A spectrometer is an instrument designed to divide light into its component colors and measure their relative intensities. Spectrometers are used as tools for many kinds of fundamental research in the sciences.  More commonly, spectrometers are vital components in color analyzers. Examples include color matching machines that identify the exact color of a paint chip, color analysis machines that provide information for the quality control of color TV tubes, and blood analyzers that measure the color of blood samples when exposed to various chemical agents.

Many spectrometers incorporate spherical concave mirrors rather than lenses to form and focus the beam of light originating at the sample. Lenses would introduce too many aberrations of color and complicate both system design and the interpretation of data. Lenses also have limited transmission in the ultraviolet and far infrared regions of the spectrum. 

A mirror with enhanced imaging quality can be designed by coating the back surface of a lens, rather than a bowed sheet of planar glass, with a reflective finish. It is similar to the cosmetic magnifying mirror, but is called a “Mangin” mirror after the man who first designed such a lens-mirror hybrid (Figure 4).

Figure 4

The image is formed by reflection and refraction in the same optical element; hence, a Mangin mirror is a catadioptric element. “Catadioptric” originates from two Greek prefixes: “kata-” meaning backwards or reflective, and “dia-” meaning through or refractive. Gas and solidstate laser manufacturers use large numbers of spherical concave mirrors. The heart of every laser is a “cavity” or “resonator” created with mirrors that face each other and reflect laser energy back and forth through an amplifying medium. Usually one of these mirrors is spherically concave to create a stable laser beam.

The quality of the image produced by a spherical concave mirror is comparable to that obtained with a single lens element. The mirror surpasses the lens in its color performance (a mirror has no aberrations of color since all colors experience the same geometry of reflection), however a mirror, like a lens, introduces spherical aberration, coma, astigmatism and curvature of field.

Limitations of image quality produced by a single spherical concave mirror can be overcome by using several complementary mirrors in a system. This is the same approach by which limitations of a single lens element are overcome by use of a compound lens. 

Catadioptric systems contain mirrors and lenses to help balance aberrations.

JML offers two grades of spherical concave mirrors: precision and commercial quality. Please see the following product list for both types of concave mirrors.

Parabolic Reflectors

In 1668, Sir Isaac Newton constructed his reflecting telescope with a parabolic mirror. He chose this design because, for narrow fields of view, a parabolic mirror will create nearly perfect images of distant objects due to its spherical correction ability.

A contemporary application can be found in the collection optics for large, collimated laser beams. A special feature of the parabolic contour is its nearly perfect focusing quality for narrow fields of view. This feature allows for simple systems design provided the field of view is small. For larger fields of view a parabolic reflector is less than ideal because it causes significant coma in the image.  In addition to serving as light-collecting elements in instruments such as telescopes, parabolic reflectors serve as optical elements in sources of light. For instance, the reflector in a flashlight is a parabola. In theory the flashlight’s beam is perfectly collimated and maintains its bright, uniform and beam-like quality over very long distances. Flashlights do not exhibit this perfect performance for two reasons. First, the source of light in a flashlight is large in comparison to the reflector’s focal length, therefore, most of the filament in the bulb lies relatively far off-axis. Second, the glass envelope around the bulb’s filament acts like a poor-quality lens and distorts the trajectories, or wavefronts, of the light rays presented to the reflector.

Another name for a parabolic mirror is “paraboloid” because its reflective surface is mathematically described as a three-dimensional surface of revolution based on a two-dimensional parabola. It is the cross-sectional view of one of these mirrors that shows a parabolic contour. Sometimes a designer needs an off-axis section of a parabolic mirror. The “off-axis” parabola is a section of a parabolic reflector. For example, a common flashlight

Figure 5

reflector is shaped like a symmetrical cup containing the light bulb. In contrast to this basic symmetry designers derive the “off axis” parabola from a segment of the parabola lying above the axis of symmetry (Figure 5).  Access to the reflecting surface is from the bottom rather than from the side allowing mechanical supporting structures at the focal point without blocking the optical path. Despite the large angle of incidence between the collimated beam and the normal to the reflector’s surface, the off-axis parabola operates at 0° field angle – i.e., the incident rays of light travel parallel to the mirror’s optical axis.

Parabolic mirrors exhibit perfect imaging for distant objects and collimated beams that are aligned with the optical axis of symmetry. Numerically controlled diamond tool machining creates the original mold for these mirrors. An electrolytic process is used to form a sheet of nickel around the mold. A thin layer of rhodium is electrolytically applied to the nickel mirror after it has been released from its mold. Rhodium is a durable and highly reflective metal. Other reflective coatings can be applied to the nickel substrates by special order.

Elliptical Reflectors

The unique imaging property of an elliptical mirror is stated in terms of its two foci; an elliptical mirror will perfectly image an object located at one focus to its other focus. An important class of application for elliptical mirrors is found in condensing systems. They can be used to collect the output of a bulb and direct it through the film gate of a projector while simultaneously focusing the filament or arc at the entrance pupil of the projection lens. Designers exploit this property to reduce the weight and complexity of specialized projection systems.

Another application for elliptical mirrors can be found in telescopes. The Gregorian telescope uses an ellipsoidal secondary mirror in conjunction with a parabolic mirror. Its shape provides an extra degree of freedom for controlling aberrations. This design is named for James Gregory, a contemporary of Sir Isaac Newton, who is credited with the invention of the reflecting telescope in the 17th century.

An ellipse has two foci (Figure 6): Focus 1 (F1) and Focus 2 (F2). The geometrical definition of an ellipse states that the sum of the distances from any one point on the curve to each focus is the same as the sum from any other point on the curve: Distance 1 + Distance 2 = constant.

Figure 6

Rays of light follow the line segments that connect each focus to a point on the ellipse. These are the same line segments that are labeled Distance 1 and Distance 2 in Figure 6. Therefore, if light emanates from one focus it will converge at the other focus (Figure 7).

Figure 7

This ray diagram depicts how a small point-object located directly on one focus will be imaged with perfect quality at the other focus. If the object has significant size (in other words, if the field of view is significantly more than zero), then aberrations will limit the quality of the image.

In practical systems the elliptical mirror is not a complete, egg-shaped ellipsoid; instead, a common elliptical mirror tends to be a small segment of the whole ellipse (Figure 8).

Figure 8

Elliptical mirrors image an object located at one focus to the other focus. For small objects, the quality of the image is nearly perfect. Numerically controlled diamond tool machining creates the original mold for these mirrors. An electrolytic process is used to form a sheet of nickel around the mold. A thin layer of rhodium is electrolytically applied to the nickel mirror after it has been released from its mold. Rhodium is durable at high temperatures and is highly reflective. Other reflective coatings can be applied to the nickel substrates by special order.

Laser

When laser engineers specify a reflecting surface they require precisely polished surface contours and high reflectance at specific wavelengths. For high-power laser applications, they also require coatings with high thresholds for laser-induced damage.

For many traditional applications involving white light, mirror surfaces are specified with quarter-wave irregularity control (ë/4). For many laser applications, engineers specify tenth-wave finishes (ë/10). Their choice concerns use of the coherent and monochromatic nature of laser light.

These two characteristics allow systems to reach diffraction-limited performance. Tenth-wave surface irregularity control for components usually eliminates manufacturing tolerance as a barrier to the realization of this goal. A narrowband mirror can reflect unpolarized light of one specific wavelength with an efficiency of about 99.0%, and must be designed for a narrow range of incident angles.

Despite these limitations, narrowband mirrors are essential elements of many laser systems. High reflectivity enables the efficient use of a laser’s output and reduces the thermal load that would be absorbed by mirrors having lower reflectivity. Additionally, dielectric mirrors can be tuned to handle specific polarizations of a laser beam and can achieve reflectivities of approximately 99.9%.

Although many applications for laser light involve power levels comparable to white-light applications, many other applications employ high-power laser beams. Dielectric mirrors with very high reflective efficiencies can also be designed to handle very high-power densities.

High-power mirrors can withstand extremely short-lived laser pulses with peak power densities of about 1 gigawatt/cm2 (1000 megawatts/cm2). In many materials this kind of power can create extremely high temperatures for very brief fractions of a second.

Engineers design high-power systems with large beams to spread the power over a large area and minimize the power densities at the reflecting and refracting surfaces. At the output of these machines, the beams are focused into tiny spots to achieve power densities greater than 100 gigawatts/cm2 (100,000  megawatts/cm²). Applications for such pulsed power include spot welding and drilling of thin metals and plastics. These lasers also can be employed in medical procedures such as ophthalmic surgery.

High-power mirrors can withstand up to 1 kilowatt/cm2 of continuous wave (CW) irradiation. Because continuous beams of laser light can cause more thermal damage than pulsed beams, the continuous power rating of a mirror is less than its pulsed power rating. Industrial applications for continuous wave lasers include welding and cutting thick plates of steel. Medical applications include substitution of a laser scalpel for the traditional knife. As with pulsed laser systems, engineers design large beam sizes for CW lasers. This design philosophy lowers the power density at the surfaces of the internal optical elements and increases their service lifetimes.

Even with reflectivities beyond 99% some laser energy will be absorbed by a reflective coating. When exposed to very high continuous power, this absorbed energy can warp the mirror’s substrate. For some applications, thermally stable substrates with low coefficients of thermal expansion, such as quartz and Pyrex®, can be employed.  For other applications, metal substrates must be used because their high coefficients of thermal conductivity allow efficient cooling of the mirror. Metal mirror substrates often contain channels for the circulation of coolants.

Hot/Cold Mirrors

Hot mirrors reflect infrared and transmit visible light. Cold mirrors behave in exactly the opposite way – reflecting visible and transmitting infrared light.  Sometimes they are referred to as dichroic mirrors, meaning “two colors.” Dichroic mirrors reflect one set of wavelengths and transmit another. Hot or cold mirrors can be used to overlay two beams of widely different wavelengths. One beam is transmitted through the surface of the mirror; the other beam is directed to reflect off the mirror. The mirror is tilted so that the reflected beam travels along the same path as the transmitted beam (Figure 9).

Figure 9

Engineers use this concept in the design of surgical lasers. The hot radiation from an infrared laser provides the power to cut tissue, but its invisible beam cannot be seen by the surgeon. A cool, visible laser beam is combined with the infrared beam to serve as a visual guide for the laser scalpel.

The terminology of hot and cold originates in the ability of long-wavelength infrared light to heat objects much more efficiently than short-wavelength light. This phenomenon is explained by quantum mechanics as the tendency for longer wavelengths to excite molecular motion that we sense as heat. Shorter wavelengths excite electrons within the atoms. We do not sense excited electrons as heat.

An application for cold mirrors can be found in some projection lamps. The back reflector is a cold mirror. It is designed to reflect brilliant white light forward to the filament and the film gate. Infrared heat is transmitted to the bulb’s housing where it is harmlessly dissipated.  In some highly efficient bulbs used for illumination a hot mirror reflects infrared heat back to the filament to boost its temperature. The white light produced by these bulbs can escape even though the infrared light is trapped

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