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Art of Aspheres

We’ll walk you through the process, and invite you to visit the Resource Library for technical resources at every step.

Prism Specification
Prism Manufacturing
Prism Testing
Prism Coatings
Prism Delivery
Prism Future

Customers trust Optimax to create high-quality optics and deliver them fast, and our custom aspheres are no exception. Designing with aspheres reduces the size and weight of your system. Optimax produces aspheres from glass, fused silica, crystals and ceramics for UV, Visible and IR applications using proprietary “grind and shine” techniques for low scatter surfaces.

Optimax Asphere Lens Manufacturing Capabilities

Aspheres have one or more optical surfaces of non-constant curvature. They have a wide range of applications and are used to manage aberrations inherent to spherical lens systems, and to reduce system size and weight. Aspheric lenses have enabled a leap forward in capabilities for medical devices and defense and security.

Manufacturing and metrology of complex aspheres is an emerging science for optical fabricators: Optimax leads the way in our investment in cutting edge equipment and testing, research and training, and track record of performance on customer programs.

Optimax Tools

Manufacturing Tolerance Chart
Test Plate Library
Preferred Glass List
Aerospace Glass List

Specifying Aspheres

Specifying an asphere begins with a custom aspheric form, often fit to the Forbes Q Polynomial (Figure 1) or the Even Aspheric Equation (Figure 2). Describing form involves specifying Vertex Radius (I/C). Conic Constant (k) and applicable Aspheric Coefficients (a). Including a Sag Table (Figure 3) provides reference information to check correct data entry for each manufacturing or metrology tool used.

Optimax places tolerances on vertex radius and form error, without tolerances on conic constant or aspheric coefficients. Even aspheric coefficients are preferred.

Need to spec or quote an asphere? Contact us or browse our technical resources:

Forbes Q Polynomial

Asphere Chart Form 1

Figure 1

Even Aspheric Equation

Forbes Q Polynomial

Figure 2

Sag Table

Asphere Chart Form3

Figure 2

Manufacturing Aspheres

Looking for the most advanced manufacturing and metrology technology in North America? Optimax utilizes deterministic CNC machine tools for predictable removal rates and adherence to tight tolerances. To control centration, precision tools maintain the optical axis.

Need to spec or quote an asphere? Contact us or browse our technical resources:

Asphere Limits

Asphere Limits
This is a graphical description of some of the terms used below.

General Comments on Manufacturing Limits

  • This represents a general list of soft limits and is intended for reference only.
  • As requirements move closer to a min or max shown the more challenging the part will be.
  • Certain combinations may not be possible – Choosing Max Sag and Min Diameter on concave surfaces for example.
  • Interferometric testing of aspheres is extremely case specific. The slower the onset of departure, the more likely interferometric testing is possible.
  • During manufacturing the lens is oversized in diameter. Be aware, forms well behaved within clear aperture may turn exotic or undefined just beyond final diameter.

Manufacturing Limits for Aspheric Surfaces

Based on Form Error Tolerance

Form Error > 2μm Lower Resolution Profilometry (2-D)1
Attribute
Minimum
Maximum
Diameter (mm) 3 250
Local Radius (mm) -8 (Concave)
Sag (mm) 0 502
Departure (mm) 0.01 20
Included Angle (°) 0 120
Form Error 0.5 – 2μm Higher Resolution Profilometry (2-D)1
Attribute
Minimum
Maximum
Diameter (mm)3 3 250
Local Radius (mm) -12 (Concave)
Sag (mm) 0 252
Departure (mm) 0.01 20
Included Angle (°) 0 150
Form Error < 0.5μm Interferometry with Stitching (3-D)
Attribute
Minimum
Maximum
Diameter (mm)3 3 250
Local Radius (mm) -13 (Concave)
Sag (mm) 0 252,4
Departure (mm) 0.002 1
Included Angle (°) 0 120+5
1Typical metrology is Zygo MetroPro plots for interferometry
2For concave surfaces the maximum may be smaller, limited by tool clearance first. Short radii have lower maximums
3Larger diameters can be accommodated using multiscan fusion
4Total sag allowed is a function of diameter, determined by fringe resolution of the interferometer
5Very basic forms (paraboloid, ellipsoid) can have higher included angles

Thin Film Coating Manufacturing Limits

Coating Capabilities
Attribute
Minimum
Maximum
Diameter 3mm 500mm
Wavelength 193nm 6000nm
Use Environment Vacuum >95% RH
Durability Moderate abrasion Severe abrasion
Measurement 68°, s, p, average polarization
Laser Damage Threshold 1064nm: >30J/cm2@10ns, >1MW/cm2CW
Layers 1 200
* Soft Tolerancing Units **Stitching/CGH dependent

General Comments on Manufacturing Limits

  • This represents a general list of soft limits and is intended for reference only.
  • As requirements move closer to a min or max shown fabrication becomes more difficult.
  • Certain combinations are unattainable, e.g. 3mm convex radius with 100mm length.
  • Certain configurations add significant fixturing costs, e.g. crossed axis cylinders, cylinders/spheres.
  • Interferometric testing of cylinders is somewhat case specific. Aperture coverage is often limited by the range of diffractive nulls available.
  • Length is always the dimension along the plano axis and width is the dimension across the power axis.

Manufacturing Limits for Cylindrical Surfaces Based on Manufacturing Method

Rod or Arbor
Attribute
Minimum
Maximum
Length (mm) 3 5001
Width (mm) Radius dependent 2 < 2x Radius
Cylinder Radius (mm) – Convex Only 2 150
X-Y
Attribute Minimum Maximum
Length (mm) 3 300
Width (mm) 2 300
Cylinder Radius (mm) 10
Concave sag to flat (mm) 0.1002 =Radius
1This is at minimum radius and width. The part-specific minimum will grow in proportion to radius.
2Flat surfaces lead to scratching problems and polisher contact issues. For both practical and economic reasons consider plano here.

Manufacturing Limits for Freeform Surfaces

Attribute
 Tolerancing Limit*
Diameter (mm) +0, -0.010
Center Thickness (mm) ± 0.050
Irregularity – Interferometry
(HeNe fringes)
0.1**
 Irregularity – Profilometry (μm)  ±1.0
 Wedge Lens – ETD (mm)
 TBD
 Surface Roughness (Å RMS)  10
* Soft Tolerancing Units **Stitching/CGH dependent

General Comments on Manufacturing Limits

    • This represents a general list of soft limits and is intended for reference only.
    • As requirements move closer to a min or max shown, the more challenging the part will be.

Manufacturing Limits for
Prism Surfaces

Attribute
Minimum
Maximum
Diameter (mm) 3 300
Thickness 1 150
Aspect Ratio1 1 502
1Diameter divided by thickness
2This represents highest values obtained. When at maximum other minimums (irregularity) may not be possible. Will be smaller with less well behaved materials.

General Comments on Manufacturing Limits

  • This represents a general list of soft limits and is intended for reference only.
  • As requirements move closer to a min or max shown, the more challenging the part will be.
  • During manufacturing, the lens is over-sized in diameter.

Manufacturing Limits for Spherical Surfaces

Based on Form Error Tolerance

Attribute
Minimum
Maximum
Diameter (mm) 3 400
Radius (mm) ±1 2
Aspect Ratio (Diameter/Center Thickness) <1:1 30:1
Included Angle (°) 0 2103
1Limited by machine envelope
2Metrology dependent. Avoid 3-10 meter radii when possible, choosing to stay plano instead. It will be less expensive too.
3This represents highest values possible. Actual value possible depends on finished and metrology options available plus tolerance range available for a given part.

Asphere Tolerancing Limits

General Comments on Tolerancing Limits

  • This represents a general list of soft limits and is intended for reference only.
  • Reducing tolerance range increases costs.
  • Optimax advises a close consideration of budget (tolerance, delivery or dollar) versus need be made prior to choosing any value below.
  • Robust sensitivity analyses will help yield the most cost-effective tolerancing.

Tolerancing Limits for Aspheric Surfaces

Attribute
Asphere Tolerancing Limit
Glass Quality (nd, vd) Melt Rebalanced and Controlled
Diameter (mm) +0, -0.010
Center Thickness (mm)6 ± 0.010 
Sag – Concave (mm)  ± 0.010 
Clear Aperture  100%7
Vertex Radius8 ± 0.1% or 3 HeNe fringes9
Irregularity – Interferometry (HeNe fringes)10 0.111
Irregularity – Profilometry (μm)10 ± 0.5 
Wedge Lens – ETD (mm)  0.00212
Bevels – Face Width @ 45° (mm)13 ± 0.05 
Scratch – Dig (MIL-PRF-13830B)14 10 – 5 
Surface Roughness (Å RMS)15 10 
6This is for the most well behaved materials. More difficult materials (CaF2, Ohara S-FPL, etc) will need larger tolerance ranges
7Of full aperture (FA)
8In addition to irregularity
9Whichever is correspondingly larger over the clear aperture
10A vertex radius tolerance is required in addition to irregularity
11As geometry requirements move closer to a min or max shown the less likely this is possible
12This specification is extremely tight and expensive. For a more economical limit, please consider using 0.005mm.
13Subject to measurement uncertainty
14Crystals and reflective materials will receive 40W inspection
15This represents lowest values obtained. Actual values for crystalline, especially polycrystalline materials, will be higher.

General Comments on Tolerancing Limits

  • This represents a general list of soft limits and is intended for reference only.
  • Reducing tolerance range increases costs.
  • Robust sensitivity analyses will help yield the most cost-effective tolerancing.

Tolerancing Limits for Cylinder Surfaces

Attribute
Cylinder Tolerancing Limit
Glass Quality (nd, vd) Melt Rebalanced and Controlled
Length and width (mm) +0, -0.020
Center Thickness (mm)3 ± 0.020 
Sag – Concave (mm)  ± 0.020 
Clear Aperture  100%4
Radius5 ± 0.1% or 3 HeNe fringes6
Irregularity – Interferometry (HeNe fringes)7 0.18
Irregularity – Profilometry (μm)  ± 0.5 
Plano Axis Wedge – ETD (mm)  0.00512
Cylinder Axis Decentration – TIR (mm)9 0.01010
Axial Twist Angle (arcminutes)  3 
Bevels – Face Width @ 45° (mm)11 0/0mm max
Scratch – Dig (MIL-PRF-13830B)12 10 – 5 
Surface Roughness (Å RMS)13 5 
3This is for the most well behaved materials. More difficult materials (CaF2, Ohara S-FPL, etc.) will need larger tolerance ranges.
4Of full aperture (FA).
5In addition to irregularity.
6Whichever is correspondingly larger over the clear aperture.
7Typical metrology is Zygo MetroPro plots for interferometry.
8As geometry requirements move closer to a min or max shown the less likely this is possible.
9Optimax measures total indicated runout (TIR) as part is rotated. Actual decentration varies with focal length.
10This specification is extremely tight and expensive. For a more economical limit, please consider using 0.0100mm.
11Subject to measurement uncertainty.
12Crystals and reflective materials will receive 40W inspection.
13This represents lowest values obtained. Actual values for crystalline, especially polycrystalline materials, will be higher.

General Comments on Tolerancing Limits

  • This represents a general list of soft limits and is intended for reference only.
  • Reducing tolerance range increases costs.
  • Robust sensitivity analyses will help yield the most cost-effective tolerancing.

Tolerancing Limits for Prism Surfaces

Attribute
Prism Tolerancing Limit
Glass Quality (nd, vd) Melt Rebalanced and Controlled
Diameter (mm) +0, -0.010
Center Thickness (mm)3 ± 0.010 
Sag – Concave (mm)  ± 0.010 
Clear Aperture  100%4
Power5 0.1 HeNe fringes6
Irregularity – Interferometry (HeNe fringes)7 0.18
Wedge Prism (window) – ETD (mm)9 0.00210
Bevels – Face Width @ 45° (mm)11 sharp 
Scratch – Dig (MIL-PRF-13830B)12 10 – 5 
Surface Roughness (Å RMS)13 4
3This is for the most well behaved materials. More difficult materials (CaF2, Ohara S-FPL, etc.) will need larger tolerance ranges.
4Of full aperture (FA)
5In addition to irregularity
6This represents lowest values obtained. Will grow with diameter. Will be larger with less well-behaved materials.
7Typical metrology is Zygo MetroPro plot for interferometry.
8This represents lowest values obtained. Will grow with diameter. Will be larger with less well-behaved materials.
9Also known as parallelism or pyramidal error in prism manufacture.
10Tighter specification is possible but can be extremely expensive. For a more economical limit, please consider using 0.005mm.
11Subject to measurement uncertainty
12Crystals and reflective materials will receive 40W inspection
13This represents lowest values obtained. Actual values for crystalline materials, especially polycrystalline, will be higher.

General Comments on Tolerancing Limits

  • This represents a general list of soft limits and is intended for reference only.
  • Reducing tolerance range increases costs.
  • Optimax advises a close consideration of budget (tolerance, delivery or dollar) versus need be made prior to choosing any value below.
  • Robust sensitivity analyses will help yield the most cost effective tolerancing.

Tolerancing Limits for Spherical Surfaces

Attribute
Sphere Tolerancing Limit
Glass Quality (nd, vd) Melt Rebalanced and Controlled
Diameter (mm) +0, -0.010
Center Thickness (mm)4 ± 0.020 
Sag – Concave (mm)  ± 0.010 
Clear Aperture  100%5
Radius (mm)6 ± 0.0025 or 1 HeNe fringe7
Irregularity (HeNe fringes)8 0.059
Wedge Lens – ETD (mm)  0.00210
Bevels – Face Width @ 45° (mm)  ± 0.0511
Scratch – Dig (MIL-PRF-13830B)12 <10 – 5 
Surface Roughness (Å RMS)  313,14
4This is for the most well behaved materials. More difficult materials (CaF2, Ohara S-FPL, etc.) will need larger tolerances ranges.
5Of full aperture (FA)
6In addition to irregularity
7Whichever is correspondingly larger over the clear aperture
8Coverage dependent, stitched or otherwise, and also subject to system error
9As geometry requirements move closer to a min or max shown the less likely this is possible
10This specification is extremely tight and expensive. For a more economical limit, please consider using 0.005mm.
11Subject to measurement uncertainty
12Crystals and reflective materials will receive 40W inspection
13This represents lowest values obtained. Actual values for crystalline, especially polycrystalline materials, will be higher.
14With scan length and filter appropriate for the selected spatial period.

Here are manufacturing limits and tolerances specific to optical aspheres, prisms, cylinders and spheres. For more detailed information on any attribute, please contact sales@optimaxsi.com.

Future Capabilities

Optimax’s R&D department is continuously looking for ways to improve our fabrication process and produce higher quality optics. Our current research projects are designed to meet future market needs, such as:

  • Conformal and freeform optics
  • Mid-spatial frequency error-free surfaces

For more information please see Optimax Innovation or contact sales@optimaxsi.com.

Technical Resources

Trials and Tribulations of Optical Manufacturing: Asphere Edition

Optimax Systems, Inc., a leader in quick delivery prototype optics, has been manufacturing aspheric lenses for more than 20 years. Along the way, we have learned many lessons and provide takeaways for other manufacturers and designers

Robotic polishing in asphere manufacturing

Optimax improved the reliability of asphere polishing platforms at a demonstrated level. Download our technical paper today to learn about our results

Make it like you use it

Testing and correcting the aspheric lens as it is used in transmission addresses some of the shortcomings of traditional 3D surface metrology. 

Profit through predictability: The MRF difference at Optimax

In an effort to reduce variation and improve predictability, Optimax integrated magnetorheological finishing into its aspheric lens manufacturing process. 

The sum of all errors: Technical Digest

The geometry of machines used to center lenses and to measure centering error all work in terms of the wedge case. Two important considerations are the centration of the lens and the difference in edge thickness. 

Specifying, Manufacturing and Measuring Aspheric Lens – Part I

A basic survey of specifying aspheric forms, function and manufacturing and testing

Specifying, Manufacturing and Measuring Aspheric Lenses – Part II

The similarities and differences between tolerancing, manufacturing and measuring spherical and aspheric surfaces are important

Practical Design Software Eases Asphere Manufacturability

Recent design methods and software advances make it much easier to design aspheric surfaces that actually work in production and test by considering manufacturability issues at the earliest possible stage in the design process

Asphere Manufacturing Considerations for the Designer

There are many topics to consider during aspheric lens design, including geometrical restrictions that hinder producing particular aspheric shapes. Understanding these restrictions will help drive cost. 

Aspheric glass lens modeling and machining

The evolution of the manufacturing technology for a specific aspheric glass lens can provide significant image quality improvement, reduction of the number of lens elements, smaller size, and lower weight. 

Introduction to Asphere Metrology

There are numerous metrology options for aspheres, including how they work, requirements, and what is specified with each method in an effort to tolerance aspheres

Aspheres: Finding the right tool: metrology for the manufacture of freeform optics

As featured in Laser Focus World: Three metrology tools for the measurement of freeform optics are compared: the coordinate measurement machine, a high-accuracy profilometer, and a noncontact optical technique called fringe reflection deflectometry

Innovation: Optimax Sponsors Slope Tolerance Webinar

Optical Society of America: Surface Slope Tolerances This webinar will describe the effects of surface slope errors – concentrating on the “mid spatial frequency” region – on image quality, and will describe methods for determining tolerances for surface slope. Presented by John Rogers, Ph.D., Synopsys Sponsored by Optimax &nbsp

What’s New: Asphere Production Cell

What: Precision asphere manufacturing lean cell Capabilities: This will allow us to create rotational symmetric aspheric lenses in production quantities. These types of lenses are used in imaging systems to reduce, size and weight while improving overall system performance. When: Cell will be operational end of

Optimax Capabilities

Expedited Optics Manufacturing & Delivery

With years of experience perfecting its Lean manufacturing processes, Optimax is uniquely qualified to offer fast, on-time deliveries.

Optimax is the world’s leading rapid delivery manufacturer of custom optical components. Since its founding, Optimax has recognized that industries and institutions need fast deliveries of high quality, precision optics and has invested more than 15 years perfecting highly reliable and effective Lean processes. To learn more about these and other Optimax innovations, please visit About Optimax.

Customers trust Optimax to reliably manufacture their most complex optics on time. In the unlikely event that an expedited delivery is late, Optimax policy is to refund any unearned premium.

When you need optics fast and right!

Optimax excels at grinding, polishing and coating precision optics quickly and reliably. We can deliver high precision optics in as little as one week.

Optimax Capabilities

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