Off-Axis Parabolic Mirrors, Protected Silver Coating

Video Insight: How to Align an Off-Axis Parabolic (OAP) Mirror 

Choosing the right mounting adapter is the first step in aligning an OAP mirror. Guidance on how to select the right mounting adapter is located below. For information on how to align an OAP mirror, watch our video to the right. 

Mounting Adapters Selection Guide

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Mounting Adapter Installation
(Smooth Bore Adapter Shown)

The bottom of each off-axis parabolic (OAP) mirror contains three tapped mounting holes in a triangle pattern and an alignment hole. These holes are used to attach our Mounting Adapters, which contain three corresponding counterbore holes or captive screws and an alignment pin (see the image to the right). Together, these features allow our OAP mirrors to be securely mounted. The tapped holes are also useful in OEM applications.

We offer three types of mounting plates for Ø1/2", Ø1", and Ø2" OAP mirrors. The first type is designed to be mounted in any Ø1", Ø2", or Ø3" mirror mount, depending upon the diameter of the OAP mirror. The second type, designed for post mounting, contains an 8-32 (M4) tapped hole on all four sides for direct mechanical compatibility with Ø1/2" Posts. The third type is externally SM threaded for direct compatibility with any of our internally SM-threaded components, such as our rotation mounts. For Ø1" 90° OAP mirrors, the KCB1P(/M) right-angle mount allows for cage system integration. The table below shows all of these options.

Our Ø1/2", Ø1", and Ø2" OAP mirrors can also be adapted to our SM threads by placing them into our SM Thread to Double Bore Adapters. This type of adapter allows rotation of the OAP mirror with respect to the adapter prior to securing its position, whereas when using the SM-threaded adapters offered on this page, the final location of the OAP mirror is dictated either by the threads themselves (when fully threaded into a mount) or by using the provided retaining ring to secure it in place.

For Ø3" OAP mirrors, we offer the SM2MP3 mounting adapter, which contains four 8-32 tapped holes for post mounting and has external SM2 threading for mounting in our SM2-threaded components, such as the K6X2 6-axis kinematic mount.

Alternatively, all of our OAP mirrors may be directly mounted in our Precision Kinematic Mirror Mounts using their outer diameter.

OAP Mirror Mounting Adapters
Adapter Type	Example Photo (Click to Enlarge)	OAP Mirror Diameter
		1/2"	1"	2"	3"
Smooth Bore		MP127P1 For Ø1" Mounts	MP254P1 For Ø2" Mounts	MP508P1a For Ø3" Mounts	-
Post Mounting		MP127P2(/M) 8-32 (M4) Taps	MP254P2(/M) 8-32 (M4) Taps	MP508P2(/M)a 8-32 (M4) Taps	SM2MP3 8-32 Taps
SM-Threaded		SM05MP External SM05 (0.535"-40)	SM1MP External SM1 (1.035"-40)	SM2MPa External SM2 (2.035"-40)	SM2MP3 External SM2 (2.035"-40)
Right-Angle OAP Mirror Mount		-	KCB1P(/M) 30 mm Cage Compatible 1/4"-20 (M6) Tap	-	-

• Please note that these mounting adapters for Ø2" OAP mirrors do not have a centered hole for a through beam parallel to the collimated beam. Our smooth bore mounting adapters can be used to mount Ø2" OAP mirrors with through holes.

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.

Testing Method

Thorlabs' LIDT testing is done in compliance with ISO/DIS 11254 and ISO 21254 specifications.

First, a low-power/energy beam is directed to the optic under test. The optic is exposed in 10 locations to this laser beam for 30 seconds (CW) or for a number of pulses (pulse repetition frequency specified). After exposure, the optic is examined by a microscope (~100X magnification) for any visible damage. The number of locations that are damaged at a particular power/energy level is recorded. Next, the power/energy is either increased or decreased and the optic is exposed at 10 new locations. This process is repeated until damage is observed. The damage threshold is then assigned to be the highest power/energy that the optic can withstand without causing damage. A histogram such as that below represents the testing of one BB1-E02 mirror.

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) [1]. 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:

1. Wavelength of your laser
2. Beam diameter of your beam (1/e²)
3. Approximate intensity profile of your beam (e.g., Gaussian)
4. Linear power density of your beam (total power divided by 1/e² beam diameter)

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.

Pulsed Lasers

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 [2]. 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:

1. Wavelength of your laser
2. Energy density of your beam (total energy divided by 1/e² area)
3. Pulse length of your laser
4. Pulse repetition frequency (prf) of your laser
5. Beam diameter of your laser (1/e² )
6. Approximate intensity profile of your beam (e.g., Gaussian)

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 [3]. 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 [4]. 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.

[1] R. M. Wood, Optics and Laser Tech. 29, 517 (1998).
[2] Roger M. Wood, Laser-Induced Damage of Optical Materials (Institute of Physics Publishing, Philadelphia, PA, 2003).
[3] C. W. Carr et al., Phys. Rev. Lett. 91, 127402 (2003).
[4] N. Bloembergen, Appl. Opt. 12, 661 (1973).

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
Suppose that a CW laser system at 1319 nm produces a 0.5 W Gaussian beam that has a 1/e² diameter of 10 mm. A naive calculation of the average linear power density of this beam would yield a value of 0.5 W/cm, given by the total power divided by the beam diameter:

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
Suppose that a pulsed Nd:YAG laser system is frequency tripled to produce a 10 Hz output, consisting of 2 ns output pulses at 355 nm, each with 1 J of energy, in a Gaussian beam with a 1.9 cm beam diameter (1/e²). The average energy density of each pulse is found by dividing the pulse energy by the beam area:

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
Suppose that a pulsed laser system emits 10 ns pulses at 2.5 Hz, each with 100 mJ of energy at 1064 nm in a 16 mm diameter beam (1/e²) that must be attenuated with a neutral density filter. For a Gaussian output, these specifications result in a maximum energy density of 0.1 J/cm². The damage threshold of an NDUV10A Ø25 mm, OD 1.0, reflective neutral density filter is 0.05 J/cm² for 10 ns pulses at 355 nm, while the damage threshold of the similar NE10A absorptive filter is 10 J/cm² for 10 ns pulses at 532 nm. As described on the previous tab, the LIDT value of an optic scales with the square root of the wavelength in the nanosecond pulse regime:

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
Consider a laser system that produces 1 µs pulses, each containing 150 µJ of energy at a repetition rate of 50 kHz, resulting in a relatively high duty cycle of 5%. This system falls somewhere between the regimes of CW and pulsed laser induced damage, and could potentially damage an optic by mechanisms associated with either regime. As a result, both CW and pulsed LIDT values must be compared to the properties of the laser system to ensure safe operation.

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.

Custom Off-Axis Parabolic (OAP) and Aspheric Mirrors

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We offer OAP mirrors with custom sizes, focal lengths, substrates, coatings, and clearance holes.

In addition to our stock off-axis parabolic (OAP) mirrors, Thorlabs is also capable of manufacturing a variety of custom aspheric mirrors. Our unique single-point diamond turning (SPDT) capabilities allow us to produce these customs in low quantities at prices that are comparable with our stock offerings. As shown in the video to the right, we engage the slow-slide-servo process of our SPDT machine to polish individual off-axis mirrors by synchronizing the rotational position of the spindle with the linear position of the translation axes.

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Toroidal mirrors have two different radii of curvature and are used to image off-axis points without introducing astigmatism.

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Conical mirrors provide 360° of illumination.

This unique manufacturing capability allows us to provide OAP mirrors with custom reflected focal lengths and diameters, including long-focal-length and large-diameter optics that cannot be produced by conventional two-axis machining. In addition, we can produce OAP mirrors with a variety of custom substrates (including copper), custom coatings, and custom hole sizes and shapes. The use of copper substrates and other advanced techniques also allow us to offer OAP mirrors with enhanced finishes that exhibit less surface roughness than our our stock products, resulting in improved wavefront quality.

Our SPDT competency also enables us to produce mirrors with other custom biconic surfaces and aspheric shapes, including on-axis parabolic, conical, and toroidal mirrors. These custom mirror shapes can be used in a wide variety of optical instruments and specialized imaging systems. For example, toroidal mirrors, which are used to image off-axis points without introducing astigmatism, are commonly used in compact Czerny-Turner monochromators. Conical mirrors, on the other hand, are ideal for non-imaging applications that require 360° of uniform illumination.

We are generally able to produce custom OAP mirrors and aspheric mirrors with short lead times. For modifications to an existing part, delivery in 4-6 weeks is standard. For custom shapes and long focal length optics, a 6-8 week lead time is typical. To receive more information or a quote for a custom optic, please contact Tech Support.

Insights into Off-Axis Parabolic Mirrors

Scroll down to read about the unique properties of off-axis parabolic (OAP) mirrors and how to take advantage of them:

• Focus Collimated Light / Collimate Light from a Point Source
• Benefits of Pairing OAP Mirrors
• Mounting and Aligning an OAP Mirror

Click here for more insights into lab practices and equipment.

Focus Collimated Light / Collimate Light from a Point Source

Parabolic and off-axis parabolic (OAP) mirrors will only provide the expected well-collimated beam or diffraction-limited focal spot when the correct beam type is incident along the proper axis. This due to the parabolic shape of these mirrors' reflective surfaces, which are not symmetric around their focal points.

Parabolic vs. Off-Axis Parabolic Mirrors
The reflective surface of an OAP mirror is a section of the parent parabola that is not centered on the parent's optical axis (Figure 1). A conventional parabolic mirror is illustrated in Figure 2.

The optical axis of an OAP mirror is parallel to, but displaced from the optical axis of the parent parabola. The focal point of the OAP mirror coincides with that of the parent parabola.

The focal axis of the OAP mirror passes through the focal point and the center of the OAP mirror. The focal and optical axes of an OAP mirror are not parallel. In contrast, these axes coincide for parabolic mirrors whose reflective surfaces are centered on optical axis of the parent parabola.

Focus Collimated Light
If a parabolic or OAP mirror is being used to focus a beam of collimated light to a diffraction-limited point, the light must be directed along the mirror's optical axis (Figures 1 and 2).

Collimated light that is not directed parallel to the optical axis will not focus to a unique point (Figure 3).

Thorlabs recommends against directing collimated light along the focal axis of OAP mirrors, or along any direction that is not parallel to the optical axis, since the light will not focus to a diffraction-limited spot.

Collimate Light from a Point Source
To obtain highly collimated light from a point source, the point source should be located at the mirror's focal point.

Light from a point source will be poorly collimated if the point source is placed along the OAP mirror's optical axis, or anywhere else that is not the focal point.

An OAP mirror can also be used to collimate a spherical wave, if its origin coincides with the focal point of the mirror.

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Figure 3: When the collimated beam is not directed along the mirror's optical axis, the mirror does not provide a diffraction-limited spot. Instead, the focal region is spread out.

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Figure 2: When the collimated beam is parallel to the optical axis of a parabolic or OAP mirror, the light focuses to a diffraction-limited spot.

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Figure 1: The focal and optical axes of an OAP mirror do not coincide and are not parallel.

Date of Last Edit: Dec. 4, 2019

Benefits of Pairing OAP Mirrors

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Figure 5: A pair of OAP mirrors can be used to couple light out of one fiber and into another. This provides access to the beam when it is necessary to insert bulk optics into the optical path. Due to the small dimension of the fiber core, light emitted from the fiber end face is similar to a point source.

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Figure 4: A pair of OAP mirrors can be used in imaging applications, and/or to relay a beam across a distance.

Relay an Image
A single OAP mirror is not recommended for finite conjugate imaging applications, when neither light beam is collimated, but a pair of OAP mirrors can successfully be used for this purpose. An example setup is illustrated in Figure 4.

The dual OAP configuration facilitates the process of adjusting the distance between mirrors. The leg of collimated light is also convenient for inserting filters and other optical elements into the beam. Another benefit is that distance between the two mirrors can be adjusted to move the focal point across the source and/or target planes without disturbing the alignment of the system.

Provide Access to the Beam in a Fiber Network
A pair of OAP mirrors can be used to create a free-space leg in an optical fiber system, which is one way to provide access to the light beam. The illustration in Figure 5 shows an example of this configuration, which can be useful when filters or other bulk optics need to be inserted into the beam path. The length of the free-space leg can be adjusted without disturbing alignment.

When setting up this system, the fibers' end faces must be aligned so that their cores coincide with the source and target focal points, respectively. The collimated beam paths of both mirrors should be co-linear and completely overlapping.

This configuration is the basis for fiber optic filter / attenuator mounts.

Date of Last Edit: Dec. 4, 2019

Mounting and Aligning an OAP Mirror

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Figure 7: When using an OAP mirror to collimate a point source, a shear plate interferometer placed in the output beam can facilitate the alignment process.

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Figure 6: The shape of the OAP mirror's reflective profile matches a section of the parent parabola that is not centered on the focal point. Due to this, the OAP's reflective surface is not rotationally symmetric. When mounting the mirror, care should be taken to ensure the mirror does not rotate around its optical axis.

OAP mirrors are not rotationally symmetric. This is due to their reflective surfaces being taken from sections of the parent parabola curve located away from the focal point (Figure 6).

Due the asymmetry of the reflector, when an OAP mirror rotates, the position of its focal point also rotates. Since this could negatively impact the performance of an optical system, the mirror should be fixed so that the reflective surface cannot rotate around its optical axis.

The optical performance of the mirror is also sensitive to alignment drift with respect to the other five degrees of freedom. One way to protect against alignment drift is to use a fixed, rather than a kinematic, mount.

Using a shear plate interferometer can be helpful when aligning an OAP mirror to an input point source. The shear plate interferometer should intercept the output beam (Figure 7), to assess its collimation quality. Alignment is optimized when the quality of the collimated beam is optimized. 

Date of Last Edit: Dec. 4, 2019