# Interference filter

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Interference filters and interference mirrors are optical components that use the effect of interference to divert light in a frequency-dependent manner , i.e. H. depending on the color for visible light, to filter or to mirror. The designation of the component as a filter or mirror depends on whether the transmitted or reflected light is used. In most cases, these components are as dielectric , thin layers constructed on a support (z. B. Bragg mirror ). There are also components in the form of Fabry-Perot interferometers .

Such a filter or mirror has a different degree of reflection and transmission for light of different wavelengths , different angles of incidence and, in some cases, different polarization .

Interference filter with wide pass bands

## Determining properties

The main characteristics are:

• The spectral transmittance is the ratio of the radiant power transmitted to the incident radiant power. This can also be specified as the optical density , which is linked to the transmittance via the formula .${\ displaystyle \ tau (\ lambda, \ mathrm {AOI}, p)}$ ${\ displaystyle D (\ lambda, \ mathrm {AOI}, p)}$${\ displaystyle \ tau (\ lambda, \ mathrm {AOI}, p) = 10 ^ {- D (\ lambda, \ mathrm {AOI}, p)}}$
• The spectral reflectance is the ratio of reflected radiation power to incident radiation power.${\ displaystyle \ rho (\ lambda, \ mathrm {AOI}, p)}$
• The spectral absorption coefficient is the ratio of the radiant power converted into another form of energy (e.g. heat) in the component to the incident radiant power.${\ displaystyle \ alpha (\ lambda, \ mathrm {AOI}, p)}$
• The spectral scatter is the sum of the non-directional (diffuse) spectral transmittance and reflectance.

each with the wavelength , the angle of incidence (AOI ) and the polarization state of the incident light . In terms of the degree of transmission and reflection, a distinction is made between the directed and the diffuse part. The directional component is used as a basis for the spectral description, while the sum of the diffuse components gives the spectral scatter. In special cases, the change in the phase relationship between the s- and p-polarized component of the incident radiation through the component plays a role. ${\ displaystyle \ lambda}$${\ displaystyle p}$

## Subdivision

The subdivision of interference filters and mirrors can take place with regard to the materials used as well as with regard to the spectral properties. With regard to the choice of material, there are essentially two different forms. Filters and mirrors in the first group use semi-transparent, i.e. very thin, metallic layers (usually two layers separated by a spacer layer, similar to a Fabry-Perot interferometer). The second group is based on the interference in a stack of mostly several dielectric layers of different materials.

With regard to their spectral properties, a distinction is made between the following filters:

• Bandpass filter : Has a high degree of transmission for a certain wavelength band , while shorter and longer wavelengths are reflected or absorbed (e.g. in color filter wheels for projectors).
• Band-stop filter : Has a low degree of transmission for a certain wavelength range, while shorter and longer wavelengths are allowed through (e.g. filters for fluorescence microscopy).
• Long-pass filter : Has a high degree of transmission for long wavelengths and a low degree of transmission for short wavelengths (e.g. cold light reflectors for halogen lamps).
• Short-pass filter : has a high degree of transmission for short wavelengths and a low degree of transmission for long wavelengths (e.g. infrared cut filter for digital cameras).
• Polarizing beam splitter: Has a high transmittance for one polarization (typically p-polarization) and a low transmittance for the orthogonal polarization (typically s-polarization).

Filters that have a different degree of transmission or reflection for two wavelength ranges are also referred to as dichroic interference filters or mirrors. Components for three wavelength ranges are called trichroic .

Interference filters can be both narrow-band filters, so-called line filters, and broad-band band filters.

## construction

In the classic sense, interference filters and mirrors are non- tunable Fabry-Pérot interferometers and consist, for example, of a thick carrier layer (glass) on which a partially transparent metallic mirror layer (e.g. silver , aluminum ) is vapor-deposited, followed by a thin dielectric layer , transparent layer and a second mirror layer (multiple interference filter). The thickness of the dielectric layer determines which wavelengths are filtered. The transmittance of the mirror layers influences the quality of the component (with thin mirror layers the maximum of the transmitted frequency band is wide and its intensity is high; this results in a low quality of the filter). ${\ displaystyle l}$

In addition, there are increasingly complex interference filters that are built up solely from dielectric (non-metallic) layers on a transparent substrate, so-called dielectric filters. As a rule, layers of two transparent materials with different refractive indices alternate on a carrier substrate , it being possible for a different thickness from layer to layer to be required. There are also cases where more than two materials are used. The thicknesses of the individual layers are between about ten and about a thousand nanometers. The lower limit of the layer thickness is usually determined by the controllability of the manufacturing process. The upper limit depends on the wavelength range in which the filter is to be used (the longer the wavelength, the thicker layers may be required). The number of layers can be between a few and several hundred, depending on the requirements of the filter. The design of such layer sequences is done today with complex simulation programs that require the optical properties (refractive index and absorption depending on the wavelength, dispersion ) of the materials to be used as input data as well as the desired transmission or reflection spectrum, possibly depending on the angle of incidence. The simulated transmission or reflection spectrum is output, possibly depending on the angle, as well as the layer sequence. There are interfaces with which a corresponding coating system can be controlled directly. The calculation is carried out in an iterative process and, depending on the complexity, can take seconds to several hours (as of 2015). In this way, even filters with complicated requirements, e.g. B. Multi-band filters, are designed and manufactured.

## Manufacturing

Layer systems for interference filters are now usually produced by cathode atomization (sputtering), especially when it comes to complex filters with high accuracy requirements. Simpler filters, e.g. B. for anti-reflective coatings are also produced by vapor deposition of layers. Thanks to better control options, both from the process analytical side and from the system side, more and more complex filters can also be manufactured by vapor deposition.

## functionality

How an interference filter or mirror works
Reflection behavior of a simple interference filter (15 nm Ag / 150 nm MgF 2 /15 nm Ag), color-coded depending on the reflection on the incident angle and the wavelength

In order to explain the mode of operation of an interference filter or mirror, a simple system of a thin, dielectric layer on a substrate is described below.

If a "light beam" enters the component, the light beam is partially transmitted (T 1 , T 2 , ...) and reflected (R 0 , R 1 , R 2 , ...) at each (optical) interface according to the Fresnel formulas . The rays hitting the surface are split up. The transmitted, refracted rays are in turn partially reflected on the underside of the layer and again hit the surface. When the reflection takes place there, some of the rays (R 1 ) leave the thin layer after refraction , the other part is reflected and experiences multiple reflections in the further course in the layer. This leads to many beams of the same frequency emerging in parallel on both sides of the component.

The interference on thin layers is preceded by beam splitting . Therefore it is also referred to as amplitude division; in contrast to interference by diffraction as in the double slit experiment, in which one speaks of wavefront division.

To make it easier to understand how it works, weak reflection is assumed first, i.e. that is, the multiple reflections are neglected. It is sufficient to consider the interference of two partial waves, for example R 0 and R 1 . The two parallel beams are now brought to interference by a converging lens (for example the eye). Due to the different path lengths of the waves in the thin layer, they show a path difference after reflection . ${\ displaystyle \ Delta}$

${\ displaystyle \ Delta = 2nl + a}$

where is the layer thickness, the refractive index of the thin layer and the path difference possibly additionally generated by the reflections. ${\ displaystyle l}$${\ displaystyle n}$${\ displaystyle a}$

The path difference results in the extinction (destructive interference) or amplification (constructive interference) of rays of certain wavelengths . The extinction and amplification of certain wavelengths depend on the selected layer thickness of the filter and the angle of incidence of the rays. ${\ displaystyle l}$${\ displaystyle \ theta}$

For complete constructive and / or destructive interference to occur, the following conditions must be met:

• The interfering rays must be closely parallel and coherent . This condition is given for the partial beams (T 1 ) and (T 2 ) as well as the partial beams (R 1 ) and (R 2 ).
• The amplitudes of the partial beams must be the same.
• The phase shift must
• (2 n −1) 180 ° (with n = 1,2,3,4, ...) for destructive interference
or
• n · 360 ° (with n = 0,1,2,3, ...) for constructive interference
be.

## Applications

### filter

A number of filters are listed below, the effect of which is based on interference effects:

• Dielectric filter : filter without metallic, but purely made of dielectric layers of certain thicknesses and alternating refractive index .
• Anti-reflective coating : (also called a coating or anti-reflective coating ) - destructive interference of the reflected rays on optical components. Improved transmission through constructive interference of certain wavelengths.

In addition to the interference filters described, there are other optical components in which interferences are used or observed. This includes the Lummer-Gehrcke plate in which light is reflected several times in a plane-parallel plate (close to the critical angle of total reflection ), exiting and interfering with it.

### mirror

#### Dichroic mirrors

Dichroic mirrors are used, for example, in larger video cameras (three CCD cameras) to split the incident light into the RGB color space , for which two such mirrors with reflection in different wavelength ranges are required (see also CCD sensor ).

The division into filters and dichroic mirrors that was common in the past is often no longer useful today because interference filters are often used in both functions at the same time. Because the light - also in a generalized sense, which also includes UV and infrared light - of those wavelengths that are not transmitted (pass through the filter) is reflected, interference filters can be used to split a light beam into two beams with complementary wavelength ranges. The interference filter acts as a filter for one (passing) beam, but as a mirror for the other, reflected beam.

Use of interference filters in digital projectors, schematic. In this example, LCD panels are used as the imager; With other imaging devices, the optical beam path is usually more complicated. Above: simple projector with filter wheel; below: high quality projector with three imagers. The components that contain interference filters are highlighted in bold type.

A very important field of application for interference filters today is digital projection technology . Here these filters are used both to separate the light into different colors and to combine images in the three primary colors into a full-color image.

In simple projectors, different colors are displayed in quick succession (sequential). For this purpose, there is a rapidly rotating filter wheel in the beam path from the light source to the imager, which carries segments from various interference filters. The three primary colors for additive color mixing , red, green and blue , are required as a minimum . Often, however, such filter wheels contain additional segments with transmission areas for cyan, yellow and white in order to increase the brightness at the expense of color saturation. Synchronous with the color change through the filter wheel, the partial images for the relevant colors are switched in the imager. Due to the sequential color display, rapid movements can lead to the so-called rainbow effect, in which the edges between light and dark objects in the picture appear to have colored edges. Another disadvantage of this technology is the poor utilization of light, because those wavelengths that cannot pass the filter wheel have to be discarded. An attempt is made to compensate for this by brightening the brightness of light parts of the image by additional light that passes through the secondary color or white segments of the filter wheel. This leads to an overall higher image brightness, but distorts the color saturation.

Higher-quality, but also more complex projectors make better use of the light from the light source by dividing it into three beams of the primary colors red, green and blue in front of the actual image generator, which are used simultaneously (in parallel). This is done with interference filters that are also used as dichroic mirrors. One of these mirrors is often used first to let the (short-wave) blue light through, while the rest of the light, which now appears yellow, is reflected at an angle of 90 °. This is again directed to a dichroic mirror, which selectively reflects the green light (medium wavelength) at an angle of 90 ° and only lets through the red part (large wavelength). The three beams are directed to three separate image generators, possibly via additional normal mirrors, which generate three partial images in the three primary colors. These are then combined again to form a common, full-color image by means of interference filters. The latter interference filters are often located on the diagonal surfaces of a glass cube, which is composed of four prisms with a triangular base. Occasionally there are further interference filters in the beam path (so-called cinema or yellow notch filters) or directly in front of the imagers (so-called trimming filters), which cut the light spectrum again in order to increase the achievable color saturation. By using three imaging devices and a prism cube, this technology is more complex and expensive, but it also delivers improved image quality with better light yield.

Interference filters are also used in a method for stereoscopic 3D projection , which is why this method is also referred to as interference filter technology.

Dichroic mirrors are used in fluorescence microscopy in order to be able to couple the stimulating light coming from an epifluorescence condenser into the optical path of the objective without obstructing the passage of the fluorescence emission. For the observation of multiply colored samples, polychroic mirrors can also be used, which have several reflecting or transmitting spectral ranges.

In addition to being used as a spectrally selective beam splitter, dichroic mirrors can also be used as beam combiners in order to e.g. B. couple several lasers with different wavelengths in a common beam path (see diode laser ).

In contrast to reflection on metal surfaces, dichroic mirrors reflect the light of one wavelength with very little loss and are therefore often used in laser technology. Because of the low-loss reflection, less power is deposited in the mirror with intensive laser beams; Dichroic mirrors can therefore also be used at very high laser powers, which would damage metal mirrors.

In the case of a dichroic dielectric mirror for laser applications, the degree of reflection can be adjusted almost arbitrarily and very precisely, depending on the wavelength, by suitable selection of the number of layers, thickness and refractive index of the dielectrics used , which is an indispensable aid for the wavelength-dependent coupling of laser beams .

For reflex sights dichroic mirrors are used to project the red laser light of the target point into the shooter's eye.

#### Cold light and heat mirror

Cold light and heat mirrors are special dichroic mirrors that have opposite effects. A heat mirror (engl. Hot mirror ) is characterized by a high transmittance in the visible and a high degree of reflection from (low transmittance) in the infrared region. A cold mirror (Engl. Cold mirror ), however, works just the opposite, it reflects visible light well and lets infrared light ( heat radiation happen), for. B. for use in cold light mirror lamps . The infrared radiation , i.e. H. the thermal radiation of the lamp passes through the reflector and the illuminated object is less heated than with metallic reflectors. This type of light source is also called a cold light source .

• Almost any transmission and reflection spectra can be produced. There is often no alternative to a steep slope at a certain wavelength.
• Angular dependence of the incident beam : The frequency band to be filtered is influenced by the angle of incidence. This angle-dependent effect of the filter can be used for fine adjustment of the wavelengths to be filtered. The frequency band shifts in the direction of shorter wavelengths. However, if the incident beam is not parallel, the quality of the filter will deteriorate.
• Temperature dependence : In the case of porous layers, changes in temperature via the atmospheric water content can, to a small extent, influence the refractive indices of the layers and thus the spectral properties.
• Low absorption coefficient : interference filters absorb i. d. Usually only a little of the incident radiation power and accordingly only heat up slightly. In contrast, the effect of classic color filters is based on the absorption of entire spectral ranges, which can lead to excessive heating of the filter, for example in lighting technology (color filters in front of halogen lamps).
• Dielectric mirrors based on interference achieve a higher reflectivity than metallic mirrors and have high damage thresholds, and are suitable for pulsed high-power lasers.
• Interference filters do not fade.
• Interference filters are more expensive than classic color filters.
• Some layer materials with good optical properties are not very scratch-resistant.
• Thick, brittle layers or high temperatures during coating are incompatible with flexible substrates.

## Norms

The ISO standard ISO 9211 (optics and photonics - optical layers) is used to specify optical interference filters . This consists of the parts

• Part 1: Terms
• Part 2: Optical properties
• Part 3: Environmental Resistance
• Part 4: Specific test methods.

The description of the filter properties of spectacle lenses is standardized in the separate standard EN ISO 13666 Ophthalmic Optics - Spectacle Lenses - Vocabulary (ISO 13666: 1998). The standard is valid in Germany as DIN standard DIN EN ISO 13666.

## Individual evidence

1. a b Wolfgang Demtröder: Laser spectroscopy: Basics and techniques . Gabler Wissenschaftsverlage, 2004, ISBN 3-540-64219-6 , p. 117 ff .
2. Heinz Haferkorn: Optics: Physical-technical basics and applications . 4th, arr. u. exp. Edition. Wiley-VCH Verlag, 2002, ISBN 3-527-40372-8 , pp. 409 .
3. ^ A b Klaus Lüders, Robert Otto Pohl: Pohl's introduction to physics: Volume 2: Electricity and optics . Gabler Wissenschaftsverlage, 2010, ISBN 978-3-642-01627-1 , §171. Interference filter , p. 287 .
4. a b ISO 9211-1: Optics and photonics - Optical layers - Part 1: Terms (ISO 9211-1: 2010), Beuth Verlag.
5. ^ Philip W. Baumeister: Optical Coating Technology . SPIE Press, Bellingham, Washington, USA 2004, ISBN 0-8194-5313-7 .
6. Bruce E. Perilloux: Thin Film Design . SPIE Press, Bellingham, Washington, USA 2002, ISBN 0-8194-4525-8 .
7. ^ Philip W Baumeister: Optical Coating Technology . SPIE Press, Bellingham, Washington, USA 2004, ISBN 0-8194-5313-7 .
8. Max J. Riedl: Optical Basics for Infrared Systems . SPIE Press, 2002, ISBN 0-8194-4499-5 , pp. 150 ff .
9. Matthew S. Brenne Holtz, Edward H. Stupp: projection displays . John Wiley & Sons, Chichester, West Sussex, UK 2008, ISBN 978-0-470-51803-8 .
10. ISO 9211-2: Optics and optical instruments - Optical layers - Part 2: Optical properties (ISO 9211-2: 1994), Beuth Verlag. This standard has been revised and the successor version is already available as DIS (Draft International Standard).
11. ISO 9211-3: Optics and photonics - Optical layers - Part 3: Environmental resistance (ISO 9211-3: 2008), Beuth Verlag.
12. ISO 9211-4: Optics and optical instruments - Optical layers - Part 4: Specific test methods (ISO 9211-4: 2006), Beuth Verlag.