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Piezoelectric Deformable Mirrors
UV-Enhanced Aluminum Coating for 250 to 450 nm
End Cap Included
DMP40-P01 Protected Silver Coated DM Integrated into an AO System.
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The piezoelectric deformable mirror mounted on its circuit board is shown above. The three piezoelectric ceramic arms used for tip and tilt correction are seen around the edges of the mirror.
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The circular keystone deformable mirror actuator array.
Thorlabs' Piezoelectric Deformable Mirror is used to correct highly distorted wavefronts. Each mirror has a Ø10 mm pupil and is available with one of two optical coatings: UV-Enhanced Aluminum for 250 to 450 nm or Protected Silver for 450 nm to 20 µm (see the Specs and Graphs tabs for performance data). These deformable mirrors are ideal for correcting distortions that result from common sources of wavefront aberrations, such as astigmatism and coma (see the Types of Aberrations tab for more details), and include separate mechanisms to adjust for tip and tilt. They can be used in conjunction with the feedback signal from our Shack-Hartmann wavefront sensors or controlled manually using the included software (see the Software tab for more details).
The front plate of each deformable mirror housing has external SM2 (2.035"-40) threads for compatibility with Thorlabs' SM2-threaded lens tubes and has four 4-40 taps that are compatible with Thorlabs' 30 mm cage systems. Each mirror is shipped with an SM2CP1 end cap to protect the mirror surface when not in use, a power supply with a location-specific power cord, USB 2.0 cable for connecting the mirror to a PC, a calibration certificate, and a quick start guide. The complete manual can be downloaded by clicking on the red document icon () next to any of the part numbers below. The control software is available for download from the Software tab.
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A schematic showing the internal structure of the deformable mirror.
Principle of Operation
Each segment is controlled independently by applying a voltage between 0 and 200 V. The surface is designed to be flat when 100 V is applied across each electrode (see the drawing to the lower right). Pure spherical shapes can be generated by applying the same voltage that is higher or lower than 100 V to each electrode. A lower voltage at one electrode will result in a locally concave mirror shape, while a higher voltage will result in a locally convex mirror shape.
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This drawing shows the response of a single segment of the deformable mirror to 0 V, 100 V, and 200 V, from left to right.
In addition to the 40 actuators, three bimorph arms provide tip/tilt adjustment (see the photo and drawing to the upper right). The top layer of each arm is part of the ceramic disk carrying the actuators and only connects to the main part of disk via a small connection point (labeled in the drawing above). The end of the arm is attached to a carrier board. A second piezoelectric layer is bonded to the bottom of each arm, configured so that one layer will shrink while the other expands as an applied voltage is increased. Applying a voltage to an arm will change the height of the mirror at the connection point. By using three mechanically identical arms, the mirror can be tilted in any direction over a ±2 mrad range (see the Specs tab). Applying the same voltage to each arm will move the mirror parallel to its surface while holding the tilt constant, which can be used for optical phase modulation.
To effectively use the deformable mirror in an adaptive optics application, the input beam must fill or overfill the pupil diameter of the deformable mirror (matching the 1/e² beam diameter to the pupil diameter is a common practice), and the defined pupil in the software for the wavefront sensor needs to be adjusted to match the pupil of the deformable mirror.
For more information on choosing the type of deformable mirror that is best for your application, please see the Selecting a DM tab.
All technical data are valid at 23 ± 5 °C and 45 ± 15% relative humidity (non-condensing).
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A diagram showing the layout of the actuators in this deformable mirror.
Deformable Mirror Hysteresis
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This graph shows a typical hysteresis curve for a DMP40 mirror undergoing spherical deformation as the voltage across all 40 mirror segments is cycled between 0 and 200 V. The hysteresis is indicated by the black line in the graph above.
HR Coating Reflectance
The shaded regions in the graphs denote the ranges over which we recommend using these optics. Please note that the reflectance outside of these bands is not as rigorously monitored in quality control, and can vary from lot to lot, especially in out-of-band regions where the reflectance is fluctuating or sloped.
UV-Enhanced Aluminum (Item #s Ending in -F01)
Protected Silver (Item #s Ending in -P01)
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Excel Spreadsheet with Raw Data for Protected Silver
Protected silver coating reflectance from 450 nm to 1 µm at 12° AOI. The coating is designed for use from 450 nm to 20 µm.
Simplified Diagram of the AO System Shown to the Left
DMP40-P01 Deformable Mirror with a Shack-Hartmann Wavefront Sensor
The sample setup below uses a Shack-Hartmann Wavefront Sensor (WFS) to measure the change in wavefront produced by a DMP40-P01 Deformable Mirror (DM). This setup was designed to help users familiarize themselves with the behavior of the DMP40 deformable mirrors, and not to provide a fully operational adaptive optics system. See the table for a list of the parts used in the system below. If you hover over a component in the image below, the corresponding item will be highlighted in the table below.
To build the system into an experimental setups for adaptive optics applications, the input collimator can be replaced with a user-supplied beam and/or a second beamsplitter can be placed just before the WFS to redirect some of the light to an experimental setup.
A software package with a graphical user interface for operating the DMP40 for adaptive optics applications can be downloaded using the link below. Driver packages are included for developers who want to extend or adapt the functionality of the device with custom applications.
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A screenshot of the deformable mirror software GUI.
Software and GUI Features
The software includes a driver package for constructing custom applications with the following software packages:
Ideally, an optical image-forming system will produce a unique image point for each object point. Any departures from this ideal theory of Gaussian (also known as paraxial or first-order) Optics are known as aberrations and can be categorized into two main types: monochromatic (single color) aberrations and chromatic (varying wavelength) aberrations. When aberrations are present, the peak intensity will be reduced and the image or laser beam propagating to a target will be blurred. Below, we will take a look at the seven primary types of aberrations, five of which are of the monochromatic variety and two of which are of the chromatic variety. Deformable mirrors are capable of removing all types of monochromatic aberrations from a wavefront to allow for the formation of an ideal, diffraction-limited image, even if optics without diffraction-limited performance are being used in the optical system.
There are five primary monochromatic aberrations, which can be further divided into two subgroups: those that deteriorate the image (spherical aberration, coma, and astigmatism) and those that deform the image (field curvature and distortion). These aberrations are a direct result of departures from first-order (i.e., sinθ≈θ) theory, which assumes the light rays make small angles with the principal axis. As soon as one wants to consider light rays incident on the periphery of a lens, the statement sinθ≈θ, which forms the basis of paraxial optics, is no longer satisfactory and one must consider more terms in the expansion:
The five primary monochromatic aberrations were first studied by Ludwig von Seidel, and hence, they are frequently referred to as the Seidel aberrations. Please note that since the expansion of sinθ is an infinite sum, the five monochromatic aberrations discussed below are not the only ones possible; there are additional higher-order aberrations that make smaller contributions to image degradation. The surface of the deformable mirror can be altered to accommodate all of these types of monochromatic aberrations.
For parallel incoming light rays, an ideal lens will be able to focus the rays to a point on the optical axis as shown in Fig. 1a; consequently, under ideal circumstances, the image of a point source that is located on the optical axis will be a bright circular disk surrounded by faint rings (see the Airy diffraction pattern shown in Fig. 1b). However, in reality, the light rays that strike a spherical converging lens far from the principal axis will be focused to a point that is closer to the lens than those light rays that strike the spherical lens near the principal axis (see Fig. 1c). Consequently, there is no single focus for a spherical lens, and the image will appear to be blurred; instead of having an Airy diffraction pattern in which nearly all the light is contained in a central bright circular spot, spherical aberration will redistribute some of the light from the central disk to the surrounding rings (see Fig. 1d), thereby reducing image contrast. Whenever spherical aberration is present, the best focus for an uncorrected lens will be somewhere between the focal planes of the peripheral and axial rays. Please note that spherical aberration only pertains to object points that are located on the optical axis.
Figure 1. Comparison of an ideal situation to one in which spherical aberration is present. (a) For a perfect lens, all incoming light rays get focused to a single point. (b) The Airy diffraction pattern corresponding to a point source that has been imaged by a perfect lens consists of a bright central spot surrounded by faint concentric rings. (c) For a real lens, light incident on the edges of a lens is refracted more than the light striking the center of the lens, and thus, there is not one unique focal point for all incident light rays. (d) Spherical aberration degrades resolution by redistributing some of the light from the central bright spot to the surrounding concentric rings.
Coma, or comatic aberration, is an image-degrading aberration associated with object points that are even slightly off axis. When an off-axis bundle of light is incident on a lens, the light will undergo different amounts of refraction depending on where it strikes the lens (see Fig. 2a); as a result, each annulus of light will focus onto the image plane at a slightly different height and with a different spot size (see Fig. 2b), thereby leading to different transverse magnifications. The resulting image of a point source, which is shown in Fig. 2c, is a complicated asymmetrical diffraction pattern with a bright central core and a triangular flare that departs drastically from the classical Airy pattern shown in Fig 1b above. The elongated comet-like structure from which this type of aberration takes its name can extend either towards or away from the optical axis depending on whether the comatic aberration is negative or positive, respectively. Due to the asymmetry that coma causes in images, many consider it to be the worst type of aberration.
Figure 2. The effects of positive coma are shown. (a) When a light source is off-axis, the various portions of the lens do not refract the light to the same point on the image plane. (b) The central region of the lens forms a point image at the vertex of the cone, while larger rings on the periphery of the lens correspond to larger comatic circles that are displaced farther from the principal axis. (c) Coma leads to a complicated asymmetrical comet-like diffraction pattern characterized by an elongated structure of blotches and arcs. Note that the diffraction pattern shown assumes no spherical aberration.
Astigmatism, like coma, is an aberration that arises when an object point is moved away from the optical axis. Under such conditions, the incident cone of light will strike the lens obliquely, leading to a refracted wavefront characterized by two principal curvatures that ultimately determine two different focal image points. Figure 3a shows the two planes one needs to consider: the tangential (also known as the meridional) plane and the sagittal plane; the tangential plane is defined by the chief ray (i.e., the light ray from the object that passes through the center of the lens) and the optical axis, while the sagittal plane is a plane that contains the chief ray and is perpendicular to the tangential plane. In addition to the chief light ray, Fig. 3a also shows two other off-axis light rays, one passing through the tangential plane and the other passing through the sagittal plane. For complex multi-element lens systems (e.g., microscope objective or ASOM system), the tangential plane remains coherent from one end of the system to the other while the sagittal plane usually changes slope as the chief ray’s propagation direction is altered by the various components in the lens system. Consequently, in general, the focal lengths associated with these planes will be different (see Fig. 3b). If the sagittal focus and the tangential focal points are coincident, then the object point is on axis and the lens is free of astigmatism. However, as the amount of astigmatism present increases, the distance between these two foci will also increase, and as a result, the image will lose definition around its edges. The presence of astigmatism will cause the ideal circular point image to be blurred into a complicated elongated diffraction pattern that appears more linelike when more astigmatism is present (see Figs. 3c and 3d).
Figure 3. The effects of astigmatism, assuming the absence of spherical aberration and coma, are illustrated. (a) The tangential and sagittal planes are shown. (b) Light rays in the tangential and sagittal planes are refracted differently, ultimately leading to two different focal planes, which are labeled as the tangential focus and sagittal focus. (c) The Airy diffraction pattern of a point source as viewed at the tangential focal plane. (d) The Airy diffraction pattern of a point source as viewed at the sagittal focal plane.
For most optical systems, the final image must be formed on a planar surface; however, in actuality, a lens that is free of all other off-axis aberrations creates an image on a curved surface known as a Petzval surface. This nominal curvature of this surface, which is known as the Petzval curvature, is the reciprocal of the lens radius. For a positive lens, this surface curves inward towards the object plane, whereas for a negative lens, the surface curves away from that plane. The field curvature aberration arises from forcing a naturally curved image surface into a flat one. For the image, the presence of field curvature makes it impossible to have both the edges and central region of the image be crisp simultaneously. If the focal plate is shifted to the vertex of the Petzval surface (Position A in Fig. 4), the central part of the image will be in focus while the outer portion of the image will be blurred, making it impossible to distinguish minor structural details in this outer region. Alternatively, if the image plane is moved to the edges of the Petzval surface (Position B in Fig. 4), the opposite effect occurs; the edges of the image will come into focus, but the central region will become blurred. The best compromise between these two extremes is to place the image plane somewhere in between the vertex and edges of the Petzval surface, but regardless of its location, the image will never appear sharp and crisp over the entire field of view.
Figure 4. Field curvature, an aberration associated with off-axis objects, arises because the best image is not formed on the paraxial image plane but on a parabolic surface called the Petzval surface. (a) Depending on the location of the focal plane along the optic axis, either the central (if at location A) or peripheral (if at location B) portions of the field of view will be in focus but not both. (b) The central portion of the image will be crisp if the image plane is located at position A. (c) The edges of the image will be sharply in focus if the image plane is located at position B.
The last of the Seidel aberrations is distortion, which is easily recognized in the absence of all other monochromatic aberrations because it deforms the entire image even though each point is sharply focused. Distortion arises because different areas of the lens usually have different focal lengths and magnifications. If no distortion is present in a lens system, the image will be a true magnified reproduction of the object (see Fig. 5b). However, when distortion is present, off-axis points are imaged either at a distance greater than normal or less than normal, leading to a pincushion (see Fig. 5a) or barrel (see Fig. 5c) shape, respectively.
Figure 5. The effects of distortion, assuming the absence of all other forms of aberration, are illustrated. (a) Positive or pincushion distortion occurs when the transverse magnification of a lens increases with the axial distance; this effect causes each image point to be displaced radially outward from the center, with the most distant points undergoing the largest displacements. (b) If no distortion is present, the image will be a scaled duplicate of the object. (c) Negative or barrel distortion occurs when the transverse magnification of a lens decreases with axial distance; in this case, each image point moves radially inward toward the center; again, the most distant points undergo the largest displacements.
The monochromatic aberrations discussed above can all be compensated for using a deformable mirror such as the one included in these adaptive optics kits. However, when a broadband light source is used, chromatic aberrations will result. Since a DM cannot compensate for these aberrations, we will only briefly mention them here. Chromatic aberrations, which come in two forms (i.e., lateral and longitudinal), arise from the variation of the index of refraction of a lens with incident wavelength. Since blue light is refracted more than red light, the lens is not capable of focusing all colors to the same focal point; therefore, the image size and focal point for each color will be slightly different, leading to an image that is surrounded by a halo. Generally, since the eye is most sensitive to the green part of the spectrum, the tendency is to focus the lens for that region; if the image plane is then moved towards (away from) the lens, the periphery of the blurred image will be tinted red (blue).
Typically, an AO system is comprised from three components: (1) a wavefront sensor, which measures these wavefront deviations, (2) a deformable mirror, which can change shape in order to modify a highly distorted optical wavefront, and (3) real-time control software, which uses the information collected by the wavefront sensor to calculate the appropriate shape that the deformable mirror should assume in order to compensate for the distorted wavefront. Together, these three components operate in a closed-loop fashion. By this, we mean that any changes caused by the AO system can also be detected by that system. In principle, this closed-loop system is fundamentally simple; it measures the phase as a function of the position of the optical wavefront under consideration, determines its aberration, computes a correction, reshapes the deformable mirror, observes the consequence of that correction, and then repeats this process over and over again as necessary if the phase aberration varies with time. Via this procedure, the AO system is able to improve optical resolution of an image by removing aberrations from the wavefront of the light being imaged.
The Wavefront Sensor:
A Shack-Hartmann wavefront sensor uses a lenslet array to divide an incoming beam into a bunch of smaller beams, each of which is imaged onto a CCD camera, which is placed at the focal plane of the lenslet array. If a uniform plane wave is incident on a Shack-Hartmann wavefront sensor (refer to Fig. 1), a focused spot is formed along the optical axis of each lenslet, yielding a regularly spaced grid of spots in the focal plane. However, if a distorted wavefront (i.e., any non-flat wavefront) is used, the focal spots will be displaced from the optical axis of each lenslet. The amount of shift of each spot’s centroid is proportional to the local slope (i.e., tilt) of the wavefront at the location of that lenslet. The wavefront phase can then be reconstructed (within a constant) from the spot displacement information obtained (see Fig. 2).
Figure 1. When a planar wavefront is incident on the Shack-Hartmann wavefront sensor's microlens array, the light imaged on the CCD sensor will display a regularly spaced grid of spots. If, however, the wavefront is aberrated, individual spots will be displaced from the optical axis of each lenslet; if the displacement is large enough, the image spot may even appear to be missing. This information is used to calculate the shape of the wavefront that was incident on the microlens array.
Figure 2. Two Shack-Hartmann wavefront sensor screen captures are shown: the spot field (left-hand frame) and the calculated wavefront based on that spot field information (right-hand frame).
Figure 3. Dynamic range and measurement sensitivity are competing properties of a Shack-Hartmann wavefront sensor. Here, f, Δy, and d represent the focal length of the lenslet, the spot displacement, and the lenslet diameter, respectively. The equations provided for the measurement sensitivity θ min and the dynamic range θmax are obtained using the small angle approximation. θmin is the minimum wavefront slope that can be measured by the wavefront sensor. The minimum detectable spot displacement Δymin depends on the pixel size of the photodetector, the accuracy of the centroid algorithm, and the signal to noise ratio of the sensor. θmax is the maximum wavefront slope that can be measured by the wavefront sensor and corresponds to a spot displacement of Δymax, which is equal to half of the lenslet diameter. Therefore, increasing the sensitivity will decrease the dynamic range and vice versa.
The four parameters that greatly affect the performance of a given Shack-Hartmann wavefront sensor are the number of lenslets (or lenslet diameter, which typically ranges from ~100 – 600 μm), dynamic range, measurement sensitivity, and the focal length of the lenslet array (typical values range from a few millimeters to about 30 mm). The number of lenslets restricts the maximum number of Zernike coefficients that a reconstruction algorithm can reliably calculate; studies have found that the maximum number of coefficients that can be used to represent the original wavefront is approximately the same as the number of lenslets. When selecting the number of lenslets needed, one must take into account the amount of distortion s/he is trying to model (i.e., how many Zernike coefficients are needed to effectively represent the true wave aberration). When it comes to measurement sensitivity θmin and dynamic range θmax, these are competing specifications (see Fig. 3 to the right). The former determines the minimum phase that can be detected while the latter determines the maximum phase that can be measured.
A Shack-Hartmann sensor’s measurement accuracy (i.e., the minimum wavefront slope that can be measured reliably) depends on its ability to precisely measure the displacement of a focused spot with respect to a reference position, which is located along the optical axis of the lenslet. A conventional algorithm will fail to determine the correct centroid of a spot if it partially overlaps another spot or if the focal spot of a lenslet falls outside of the area of the sensor assigned to detect it (i.e., spot crossover). Special algorithms can be implemented to overcome these problems, but they limit the dynamic range of the sensor (i.e., the maximum wavefront slope that can be measured reliably). The dynamic range of a system can be increased by using a lenslet with either a larger diameter or a shorter focal length. However, the lenslet diameter is tied to the needed number of Zernike coefficients; therefore, the only other way to increase the dynamic range is to shorten the focal length of the lenslet, but this in turn, decreases the measurement sensitivity. Ideally, choose the longest focal length lens that meets both the dynamic range and measurement sensitivity requirements.
The Shack-Hartmann wavefront sensor is capable of providing information about the intensity profile as well as the calculated wavefront. Be careful not to confuse these. The left-hand frame of Fig. 4 shows a sample intensity profile, whereas the right-hand frame shows the corresponding wavefront profile. It is possible to obtain the same intensity profile from various wavefunction distributions.
Figure 4. Several pieces of information are provided by the Shack-Hartmann wavefront sensor, including information about the total power at each lenslet and the calculated wavefront distribution present. Here, the left-hand frame shows a sample intensity profile, while the right-hand frame shows the corresponding wavefront.
The Deformable Mirror:
Figure 5. The aberration compensation capabilities of a flat and MEMS deformable mirror are compared. (a) If an unaberrated wavefront is incident on a flat mirror surface, the reflected wavefront will remain unaberrated. (b) A flat mirror is not able to compensate for any deformations in the wavefront; therefore, an incoming highly aberrated wavefront will retain its aberrations upon reflection. (c) A MEMS deformable mirror is able to modify its surface profile to compensate for aberrations; the DM assumes the appropriate conjugate shape to modify the highly aberrated incident wavefront so that it is unaberrated upon reflection.
Figure 6. Cross sectional schematics of the main components of BMC's continuous (left) and segmented (right) MEMS deformable mirrors.
The range of wavefronts that can be corrected by a particular DM is limited by the actuator stroke and resolution, the number and distribution of actuators, and the model used to determine the appropriate control signals for the DM; the first two are physical limitations of the DM itself, whereas the last one is a limitation of the control software. The actuator stroke is another term for the dynamic range (i.e., the maximum displacement) of the DM actuators and is typically measured in microns. Inadequate actuator stroke leads to poor performance and can prevent the convergence of the control loop. The number of actuators determines the number of degrees of freedom that the mirror can correct for. Although many different actuator arrays have been proposed, including square, triangular, and hexagonal, most DMs are built with square actuator arrays, which are easy to position on a Cartesian coordinate system and map easily to the square detector arrays on the wavefront sensors. To fit the square array on a circular aperture, the corner actuators are sometimes removed (e.g., the deformable mirror included with the AOK1-UM01 or AOK1-UP01 has a 12 x 12 actuator configuration but only 140 actuators since the corner ones are not used). Although more actuators can be placed within a given area using some of the other configurations, the additional fabrication complexity usually does not warrant that choice.
Figure 7. A cross-like pattern is created on the DM surface by applying the voltages necessary for maximum deflection of the 44 actuators that comprise the middle two rows and middle two columns of the array. The frame on the left shows a screen shot of the AO kit software depicting the DM surface, whereas the frame on the right, which was obtained through quasi-dark field illumination, shows the actual DM surface when programmed to these settings. Note that the white light source used for illumination is visible in the lower right-hand corner of the photograph.
Figure 7 (left frame) shows a screen shot of a cross formed on the 12 x 12 actuator array of the DM included with the adaptive optics kit. To create this screen shot, the voltages applied to the middle two rows and middle two columns of actuators were set to cause full deflection of the mirror membrane. In addition to the software screen shot depicting the DM surface, quasi-dark field illumination was used to obtain a photograph of the actual DM surface when programmed to these settings (see Fig. 7, right frame)
The Control Software:
In essence, the control software uses the spot field deviations to reconstructs the phase of the beam (in this case, using Zernike polynomials) and then sends conjugate commands to the DM. A least-squares fitting routine is applied to the calculated wavefront phase in order to determine the effective Zernike polynomial data outputted for the end user. Although not the only form possible, Zernike polynomials provide a unique and convenient way to describe the phase of a beam. These polynomials form an orthogonal basis set over a unit circle with different terms representing the amount of focus, tilt, astigmatism, comma, et cetera; the polynomials are normalized so that the maximum of each term (except the piston term) is +1, the minimum is –1, and the average over the surface is always zero. Furthermore, no two aberrations ever add up to a third, thereby leaving no doubt about the type of aberration that is present.
Damage Threshold Data for DMP40-P01 Deformable Mirrors
The specifications to the right apply to Thorlabs' Piezoelectric Deformable Mirrors. Please note that the damage threshold is affected by the thin, flexible design of the mirrors and is lower than the damage threshold for our other mirrors that use Thorlabs' standard metallic coatings.
Laser Induced Damage Threshold Tutorial
The following is a general overview of how laser induced damage thresholds are measured and how the values may be utilized in determining the appropriateness of an optic for a given application. When choosing optics, it is important to understand the Laser Induced Damage Threshold (LIDT) of the optics being used. The LIDT for an optic greatly depends on the type of laser you are using. Continuous wave (CW) lasers typically cause damage from thermal effects (absorption either in the coating or in the substrate). Pulsed lasers, on the other hand, often strip electrons from the lattice structure of an optic before causing thermal damage. Note that the guideline presented here assumes room temperature operation and optics in new condition (i.e., within scratch-dig spec, surface free of contamination, etc.). Because dust or other particles on the surface of an optic can cause damage at lower thresholds, we recommend keeping surfaces clean and free of debris. For more information on cleaning optics, please see our Optics Cleaning tutorial.
Thorlabs' LIDT testing is done in compliance with ISO/DIS 11254 and ISO 21254 specifications.
The photograph above is a protected aluminum-coated mirror after LIDT testing. In this particular test, it handled 0.43 J/cm2 (1064 nm, 10 ns pulse, 10 Hz, Ø1.000 mm) before damage.
According to the test, the damage threshold of the mirror was 2.00 J/cm2 (532 nm, 10 ns pulse, 10 Hz, Ø0.803 mm). Please keep in mind that these tests are performed on clean optics, as dirt and contamination can significantly lower the damage threshold of a component. While the test results are only representative of one coating run, Thorlabs specifies damage threshold values that account for coating variances.
Continuous Wave and Long-Pulse Lasers
When an optic is damaged by a continuous wave (CW) laser, it is usually due to the melting of the surface as a result of absorbing the laser's energy or damage to the optical coating (antireflection) . Pulsed lasers with pulse lengths longer than 1 µs can be treated as CW lasers for LIDT discussions.
When pulse lengths are between 1 ns and 1 µs, laser-induced damage can occur either because of absorption or a dielectric breakdown (therefore, a user must check both CW and pulsed LIDT). Absorption is either due to an intrinsic property of the optic or due to surface irregularities; thus LIDT values are only valid for optics meeting or exceeding the surface quality specifications given by a manufacturer. While many optics can handle high power CW lasers, cemented (e.g., achromatic doublets) or highly absorptive (e.g., ND filters) optics tend to have lower CW damage thresholds. These lower thresholds are due to absorption or scattering in the cement or metal coating.
Pulsed lasers with high pulse repetition frequencies (PRF) may behave similarly to CW beams. Unfortunately, this is highly dependent on factors such as absorption and thermal diffusivity, so there is no reliable method for determining when a high PRF laser will damage an optic due to thermal effects. For beams with a high PRF both the average and peak powers must be compared to the equivalent CW power. Additionally, for highly transparent materials, there is little to no drop in the LIDT with increasing PRF.
In order to use the specified CW damage threshold of an optic, it is necessary to know the following:
Thorlabs expresses LIDT for CW lasers as a linear power density measured in W/cm. In this regime, the LIDT given as a linear power density can be applied to any beam diameter; one does not need to compute an adjusted LIDT to adjust for changes in spot size, as demonstrated by the graph to the right. Average linear power density can be calculated using the equation below.
The calculation above assumes a uniform beam intensity profile. You must now consider hotspots in the beam or other non-uniform intensity profiles and roughly calculate a maximum power density. For reference, a Gaussian beam typically has a maximum power density that is twice that of the uniform beam (see lower right).
Now compare the maximum power density to that which is specified as the LIDT for the optic. If the optic was tested at a wavelength other than your operating wavelength, the damage threshold must be scaled appropriately. A good rule of thumb is that the damage threshold has a linear relationship with wavelength such that as you move to shorter wavelengths, the damage threshold decreases (i.e., a LIDT of 10 W/cm at 1310 nm scales to 5 W/cm at 655 nm):
While this rule of thumb provides a general trend, it is not a quantitative analysis of LIDT vs wavelength. In CW applications, for instance, damage scales more strongly with absorption in the coating and substrate, which does not necessarily scale well with wavelength. While the above procedure provides a good rule of thumb for LIDT values, please contact Tech Support if your wavelength is different from the specified LIDT wavelength. If your power density is less than the adjusted LIDT of the optic, then the optic should work for your application.
Please note that we have a buffer built in between the specified damage thresholds online and the tests which we have done, which accommodates variation between batches. Upon request, we can provide individual test information and a testing certificate. The damage analysis will be carried out on a similar optic (customer's optic will not be damaged). Testing may result in additional costs or lead times. Contact Tech Support for more information.
As previously stated, pulsed lasers typically induce a different type of damage to the optic than CW lasers. Pulsed lasers often do not heat the optic enough to damage it; instead, pulsed lasers produce strong electric fields capable of inducing dielectric breakdown in the material. Unfortunately, it can be very difficult to compare the LIDT specification of an optic to your laser. There are multiple regimes in which a pulsed laser can damage an optic and this is based on the laser's pulse length. The highlighted columns in the table below outline the relevant pulse lengths for our specified LIDT values.
Pulses shorter than 10-9 s cannot be compared to our specified LIDT values with much reliability. In this ultra-short-pulse regime various mechanics, such as multiphoton-avalanche ionization, take over as the predominate damage mechanism . In contrast, pulses between 10-7 s and 10-4 s may cause damage to an optic either because of dielectric breakdown or thermal effects. This means that both CW and pulsed damage thresholds must be compared to the laser beam to determine whether the optic is suitable for your application.
When comparing an LIDT specified for a pulsed laser to your laser, it is essential to know the following:
The energy density of your beam should be calculated in terms of J/cm2. The graph to the right shows why expressing the LIDT as an energy density provides the best metric for short pulse sources. In this regime, the LIDT given as an energy density can be applied to any beam diameter; one does not need to compute an adjusted LIDT to adjust for changes in spot size. This calculation assumes a uniform beam intensity profile. You must now adjust this energy density to account for hotspots or other nonuniform intensity profiles and roughly calculate a maximum energy density. For reference a Gaussian beam typically has a maximum energy density that is twice that of the 1/e2 beam.
Now compare the maximum energy density to that which is specified as the LIDT for the optic. If the optic was tested at a wavelength other than your operating wavelength, the damage threshold must be scaled appropriately . A good rule of thumb is that the damage threshold has an inverse square root relationship with wavelength such that as you move to shorter wavelengths, the damage threshold decreases (i.e., a LIDT of 1 J/cm2 at 1064 nm scales to 0.7 J/cm2 at 532 nm):
You now have a wavelength-adjusted energy density, which you will use in the following step.
Beam diameter is also important to know when comparing damage thresholds. While the LIDT, when expressed in units of J/cm², scales independently of spot size; large beam sizes are more likely to illuminate a larger number of defects which can lead to greater variances in the LIDT . For data presented here, a <1 mm beam size was used to measure the LIDT. For beams sizes greater than 5 mm, the LIDT (J/cm2) will not scale independently of beam diameter due to the larger size beam exposing more defects.
The pulse length must now be compensated for. The longer the pulse duration, the more energy the optic can handle. For pulse widths between 1 - 100 ns, an approximation is as follows:
Use this formula to calculate the Adjusted LIDT for an optic based on your pulse length. If your maximum energy density is less than this adjusted LIDT maximum energy density, then the optic should be suitable for your application. Keep in mind that this calculation is only used for pulses between 10-9 s and 10-7 s. For pulses between 10-7 s and 10-4 s, the CW LIDT must also be checked before deeming the optic appropriate for your application.
Please note that we have a buffer built in between the specified damage thresholds online and the tests which we have done, which accommodates variation between batches. Upon request, we can provide individual test information and a testing certificate. Contact Tech Support for more information.
 R. M. Wood, Optics and Laser Tech. 29, 517 (1998).
In order to illustrate the process of determining whether a given laser system will damage an optic, a number of example calculations of laser induced damage threshold are given below. For assistance with performing similar calculations, we provide a spreadsheet calculator that can be downloaded by clicking the button to the right. To use the calculator, enter the specified LIDT value of the optic under consideration and the relevant parameters of your laser system in the green boxes. The spreadsheet will then calculate a linear power density for CW and pulsed systems, as well as an energy density value for pulsed systems. These values are used to calculate adjusted, scaled LIDT values for the optics based on accepted scaling laws. This calculator assumes a Gaussian beam profile, so a correction factor must be introduced for other beam shapes (uniform, etc.). The LIDT scaling laws are determined from empirical relationships; their accuracy is not guaranteed. Remember that absorption by optics or coatings can significantly reduce LIDT in some spectral regions. These LIDT values are not valid for ultrashort pulses less than one nanosecond in duration.
A Gaussian beam profile has about twice the maximum intensity of a uniform beam profile.
CW Laser Example
However, the maximum power density of a Gaussian beam is about twice the maximum power density of a uniform beam, as shown in the graph to the right. Therefore, a more accurate determination of the maximum linear power density of the system is 1 W/cm.
An AC127-030-C achromatic doublet lens has a specified CW LIDT of 350 W/cm, as tested at 1550 nm. CW damage threshold values typically scale directly with the wavelength of the laser source, so this yields an adjusted LIDT value:
The adjusted LIDT value of 350 W/cm x (1319 nm / 1550 nm) = 298 W/cm is significantly higher than the calculated maximum linear power density of the laser system, so it would be safe to use this doublet lens for this application.
Pulsed Nanosecond Laser Example: Scaling for Different Pulse Durations
As described above, the maximum energy density of a Gaussian beam is about twice the average energy density. So, the maximum energy density of this beam is ~0.7 J/cm2.
The energy density of the beam can be compared to the LIDT values of 1 J/cm2 and 3.5 J/cm2 for a BB1-E01 broadband dielectric mirror and an NB1-K08 Nd:YAG laser line mirror, respectively. Both of these LIDT values, while measured at 355 nm, were determined with a 10 ns pulsed laser at 10 Hz. Therefore, an adjustment must be applied for the shorter pulse duration of the system under consideration. As described on the previous tab, LIDT values in the nanosecond pulse regime scale with the square root of the laser pulse duration:
This adjustment factor results in LIDT values of 0.45 J/cm2 for the BB1-E01 broadband mirror and 1.6 J/cm2 for the Nd:YAG laser line mirror, which are to be compared with the 0.7 J/cm2 maximum energy density of the beam. While the broadband mirror would likely be damaged by the laser, the more specialized laser line mirror is appropriate for use with this system.
Pulsed Nanosecond Laser Example: Scaling for Different Wavelengths
This scaling gives adjusted LIDT values of 0.08 J/cm2 for the reflective filter and 14 J/cm2 for the absorptive filter. In this case, the absorptive filter is the best choice in order to avoid optical damage.
Pulsed Microsecond Laser Example
If this relatively long-pulse laser emits a Gaussian 12.7 mm diameter beam (1/e2) at 980 nm, then the resulting output has a linear power density of 5.9 W/cm and an energy density of 1.2 x 10-4 J/cm2 per pulse. This can be compared to the LIDT values for a WPQ10E-980 polymer zero-order quarter-wave plate, which are 5 W/cm for CW radiation at 810 nm and 5 J/cm2 for a 10 ns pulse at 810 nm. As before, the CW LIDT of the optic scales linearly with the laser wavelength, resulting in an adjusted CW value of 6 W/cm at 980 nm. On the other hand, the pulsed LIDT scales with the square root of the laser wavelength and the square root of the pulse duration, resulting in an adjusted value of 55 J/cm2 for a 1 µs pulse at 980 nm. The pulsed LIDT of the optic is significantly greater than the energy density of the laser pulse, so individual pulses will not damage the wave plate. However, the large average linear power density of the laser system may cause thermal damage to the optic, much like a high-power CW beam.
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The circular keystone actuator array used by the piezoelectric deformable mirror.
Ideally, the deformable mirror needs to assume a surface shape that is complementary to, but half the amplitude of, the aberration profile in order to compensate for the aberrations and yield a flat wavefront. However, the actual range of wavefronts that can be corrected by a particular deformable mirror is limited by several factors:
The first four considerations are physical limitations of the deformable mirror itself, whereas hysteresis may be a limitation of the control software and/or a physical limitation of the mirror itself. Additionally, the wavelength range of the deformable mirror coating and any protective windows installed in the mirror head must be appropriate for the application wavelength.
Thorlabs' piezoelectric deformable mirrors provide a larger stroke, and therefore are able to correct for larger wavefront deviations, than our MEMS-based deformable mirrors. However, they contain a lower density of actuators over the active area of the mirror than the MEMS-based Multi DMs below, which means they cannot correct wavefront deviations on as fine of a spatial scale as the MEMS-based DMs.
To correct for both large amplitude and small spatial scale wavefront distortions, consider using a piezoelectric and MEMS-based deformable mirror in tandem, typically referred to in the literature as a woofer-tweeter configuration. The piezoelectric deformable mirror can correct for the tip, tilt, and lower order (lower spatial frequency) wavefront distortions, while the MEMS-based device compensates for higher order (higher spatial frequency) wavefront distortions. In nature, lower order wavefront distortions typically have larger magnitudes than do higher order wavefront distortions. Therefore, the combination of our lower actuator count, larger displacement, piezo-based DM and the higher actuator count, smaller displacement, MEMS-based DM is well suited to be used in a woofer-tweeter configuration.