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As we move away from this wavelength, the diffraction efficiency drops, sending light into other diffractive orders. The light that goes into the nondesign orders can propagate through the system and end up on the image plane as stray light. Contrast reduction in the image can occur if the light from the nondesign orders is sufficiently spread out such that it creates an increased background level on the area of interest of the image plane.

Reduced contrast generally results in less ability to see the fine details in the image.

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The amount of detail produced by an optical system is generally described by the modulation transfer function of the system. The reduction in MTF due to imperfect diffraction efficiency can be predicted, as has been described by multiple authors. It may be that such features result in unacceptable performance, forcing the removal of the diffractive surface and requiring alternate means of color correction or living with larger amounts of chromatic aberration.

We strongly suggest prototyping and testing systems with diffractive surfaces to verify that their diffractive artifacts are acceptable. The prototype should be tested under similar conditions to which the system is expected to be used.

Many times, under conditions of relatively uniform scene brightness, the artifacts will not be noticeable and the reduction in MTF allowable. However, under conditions with significant variation in brightness, such as an illuminated street lamp against a night sky, or high-contrast text black letters and white background or the reverse , the artifacts may be found to be unacceptable. Similar to an aspheric surface, the location of the diffractive surface within the system determines which chromatic aberrations it controls.

A diffractive surface that is placed at the aperture stop or equivalently at the pupils introduces only axial color. A diffractive surface that is placed away from the aperture stop or pupils will affect both axial and lateral color. The further the diffractive is from the stop, the larger the leverage it has on lateral color. As with aspheric surfaces, diffractive surfaces in a design should be evaluated for manufacturability and necessity. In regard to manufacturability, this generally means ensuring that the period of the grating, also known as the zone width or groove width, is sufficiently large.

For production of diffractive mold masters by standard machining methods e. While smaller zones can be fabricated, these may require alternate methods, such as lithography, which may limit the sag of the surface the diffractive is placed upon, possibly forcing it to be planar. In addition, if the diffractive grooves become only several times the wavelength of light they will be used with, electromagnetic vector effects may come into play, invalidating the use of ray tracing in the design of the diffractive. With regard to necessity, it should be verified that adequate color correction cannot be achieved for a given number of lenses without the use of the diffractive surface.

In general, it is best to use only one diffractive surface within a system. The use of more than one kinoform should be evaluated carefully, as multiple diffractives increase the potential for transmission loss and diffraction efficiency issues. There is always some variation between the part that is produced and the nominal design parameter values.

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Ideally, the system optical design would be highly insensitive to variation of the parts and assembly from the nominal condition. In reality, the variation of the part and assembly parameters usually limits the ultimate performance of the system. In order to develop systems that can realistically and cost-effectively be produced, a tolerance analysis needs to be performed. Tolerance analyses are used to evaluate the sensitivity of the system performance to the various tolerances associated with producing and assembling its elements.

Additionally, they can provide predictions of the range of expected performance within a batch of manufactured systems. Examples of component parameters are surface radii and center thickness, while examples of assembly parameters are lens decentration and lens spacing. Tolerance sensitivity analysis can be performed manually, by changing individual parameters and determining the effect on system performance.

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However, this is generally not necessary, as optical design codes have tolerance analysis features that allow automated tolerance sensitivity evaluation. The designer can enter a set of expected tolerances and the design software will rapidly evaluate the performance against them. There are multiple default performance criteria that the software can evaluate against, including MTF and wavefront error. Other performance criteria, such as ensquared energy, are not usually default selections.

These alternate types of criteria may need to be correlated to the default criteria or can be evaluated directly using user-defined software scripts. In addition to evaluating the performance change due to a set of defined tolerance values, the programs can also determine the magnitude of a tolerance that induces a certain drop in performance.

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Using the program in this manner allows the designer to determine which parameters are the most sensitive. This information can be fed back into the design process in an attempt to reduce or redistribute tolerance sensitivities, which generally produces more cost-effective and manufacturable designs.

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  8. With the sampled imperfection values applied, the performance of the system is evaluated. Repeating this process many times leads to a distribution of predicted system performance. Monte Carlo evaluations generally provide more reliable performance distributions than the predictions from a tolerance sensitivity analysis.

    This is because more realistic systems are evaluated, as opposed to the statistical evaluation performed during the tolerance sensitivity analysis. However, Monte Carlo evaluations do take significantly longer to perform. We recommend using both tolerance sensitivity and Monte Carlo evaluations during the development of the design. The sensitivity analyses can provide feedback into which tolerances need to be controlled, while the Monte Carlo analysis can estimate performance range and yield.

    By processing images through the nominal design, as well as through representative as-built systems which can be obtained through the Monte Carlo process above , the customer and designer can be provided with visual examples of the expected range of performance of the manufactured systems. Most customers and most designers as well have difficulty relating an image quality metric such as MTF or wavefront error to the actual system imaging performance. In this respect, the use of image simulation features allows a more intuitive feeling for the system performance.

    The input image can be provided by the customer or selected based on the intended system application. For instance, a cell phone camera may be used to take pictures of a building when touring a university.

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    Based on this, we believe that image simulation features are excellent tools for use in design trades for systems with and without molded optics. References 1. Smith, W. Modern optical engineering. New York: McGraw-Hill. Hecht, E. Reading, MA: Addison-Wesley. Fischer, R. Tadic-Galeb, and P. Optical system design. Jenkins, F.

    Fundamentals of optics. Shannon, R. The art and science of optical design. New York: Cambridge University Press. Modern lens design. Kingslake, R. Lens design fundamentals. San Diego: Academic Press. Kidger, M. Fundamental optical design. Intermediate optical design. Forbes, G. Shape specification for axially symmetric optical surfaces.