Eckhardt Optics designs and manufactures custom lenses. We’ve put together these resources to help you understand the terms and methods used in optical engineering from lens design and optical testing to illumination and optical scattering.
Whether you’re specifying a custom lens for the first time or interpreting test data, these pages are written to give you the background you need. If optics is new to you, our page on basic optics terms is a good place to start.
Optical design is the process of choosing the right lens shapes, materials, and arrangement to create the image you need. The fundamentals are the same whether you’re building a drone camera lens, a CubeSat payload, or a scatterometer: you’re controlling how light bends through glass and air to form a sharp image at the image sensor. The pages in this section cover those fundamentals — from basic optics terminology and f-numbers to resolution limits, aberrations, and manufacturing cost. We’ve also included worked examples from systems we’ve designed.
Different parts of the electromagnetic spectrum pass through the atmosphere more easily than others. This page covers the key transmission windows, from visible through LWIR, and why they matter when choosing wavelengths for remote sensing and imaging.
Light is just one small part of the electromagnetic spectrum, which extends from radio waves through microwaves, infrared, visible, ultraviolet, X-rays and gamma rays. Optics deals with wavelengths from the infrared through the ultraviolet. Knowing which part of this spectrum is best for your application is a prerequisite for the optical design.
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The choice of glass (or crystal, or plastic) determines what wavelengths a lens can transmit, how much chromatic aberration it will have, and how it responds to temperature changes. Common optical glasses like BK7 and fused silica work well in the visible spectrum, while materials like germanium, zinc selenide, and chalcogenides are used for infrared applications. Material selection is one of the first decisions in any lens design.
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Without coatings, each glass-air surface in a lens reflects about 4% of the light. In a multi-element lens, those losses add up quickly, and the reflected light becomes stray light that reduces contrast. Anti-reflection coatings reduce these losses, while other coating types (mirrors, filters, beamsplitters) are designed to reflect or transmit specific wavelengths. The choice of coating depends on the wavelength range, angle of incidence, and environmental requirements.
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This page walks through the fundamental vocabulary of lens design using a simple lens diagram: positive and negative lenses, object and image distance, marginal and chief rays, magnification, and f-number. If you’re new to optics or need a quick refresher, start here.
The aperture stop is the physical opening that limits how much light gets through a lens. The entrance pupil and exit pupil are images of that stop formed by the surrounding optics. Understanding stops and pupils is essential for controlling light gathering capability, chief ray angle, and telecentricity.
F-number and numerical aperture both describe how much light a lens can collect, but they come from different traditions — f/# from photography and NA from microscopy. This page defines each, shows how they’re related, and explains when the simple approximation between them starts to break down.
With an understanding of the basic concepts, you’re ready for an example. Lenses for machine vision are a good place to start. The linked page discusses imaging system design, covering sensor selection and the optical parameters that determine system-level performance. As a bonus, it includes a helpful calculator.
Ground sampling distance (GSD) ties together focal length, pixel size, and platform altitude to determine spatial resolution in a remote sensing system. This page walks through the calculation with worked examples for drones and CubeSats. It includes a calculator you can use for your remote sensing lens.
For application-specific guidance, see our pages on custom lenses for drones, how to specify a drone lens, and optical systems for CubeSats.
Even a perfectly made lens produces an imperfect image. These imperfections, aberrations, are divided into two categories: chromatic (caused by wavelength-dependent refraction) and monochromatic (caused by geometry). This page covers each of the major aberrations with diagrams and equations.
Any deviation of an image from its ideal shape is called distortion. This page covers the two main types (f·tan(θ) and f·θ) and adds stereoscopic, which assures that the image of a sphere is always a circle. If you’re working with conoscopic lenses or remote sensing systems where angle-to-position mapping matters, f·θ distortion is particularly relevant.
How small a detail can your lens resolve? The answer depends on aperture, and the definitions go back to Lord Rayleigh and Ernst Abbe in the 19th century. This page covers the Rayleigh criterion, Dawes’ limit, and the relationship between linear resolution (used in microscopy) and angular resolution (used in telescopes).
We’re often asked, “what MTF is good enough?” The answer is, of course, “it depends” — but when MTF drops below about 0.2, the image is probably unacceptable. This page explains what MTF actually measures: how contrast changes across spatial frequencies, from coarse detail to fine. It starts with an intuitive analogy to printer DPI and works up to the full definition.
Through-focus MTF shows how contrast changes as you shift the image plane through best focus. It’s useful for understanding depth of focus and how aberrations like spherical and chromatic affect real-world performance.
If you’re in a hurry, start by assuming each prototype lens element or prism costs about $2,000. At the other extreme, production plastic lenses can be closer to $2. The answer for your application depends on many factors — number of elements, glass types, tolerances, coatings, and volume. This page breaks down the major cost drivers.
Every dimension on a lens drawing has a tolerance — the acceptable range of variation from the ideal value. Tighter tolerances mean better performance but higher cost. The art of tolerancing is finding the balance: which parameters matter most for your application, and how loose can the rest be without degrading the image? Surface form, thickness, centration, and index of refraction all play a role.
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Dozens of lens types exist, so how do you know which one you need? This page maps them on a chart of f/# versus field of view — an idea credited to Warren Smith in Modern Optical Engineering — and links to detailed pages on telescopes, microscopes, camera lenses, conoscopes, and more.
What do lens designers really do? This page walks through the process from specification and first-order layout through optimization, tolerancing, and prototype evaluation.
Our recommended reading list for anyone learning or working in optical engineering, from introductory textbooks to advanced references on lens design, radiometry, and optical testing.
The goal of optical testing is to determine if a lens, mirror, or optical system is good enough. There are many ways to answer that question — from measuring resolution and distortion on a finished assembly to evaluating individual element surface quality.
The most complete measure of lens performance is MTF testing, which captures contrast across all spatial frequencies. The pages in this section will help you understand the most common test methods and interpret the data we deliver with your optics.
A starting point for understanding the landscape of optical testing — what gets measured on individual lens elements (surface form, centration, roughness) versus what gets tested on assembled systems (resolution, MTF, wavefront). This page maps out the methods covered in detail below.
Surface form describes how closely the actual shape of a polished lens surface matches the intended shape — whether that’s a sphere, asphere, or flat. Deviations are typically measured in fractions of a wavelength using an interferometer. A surface that’s specified to λ/4 must match the design shape to within about 160 nanometers at visible wavelengths.
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A lens element is properly centered when its optical axis aligns with its mechanical axis. Centration is measured in terms of the angular displacement between the two axes, typically specified in arcminutes. It is important because decentered elements can be make assembly difficult.
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Although scratches and digs on a lens surface are mostly cosmetic, they can scatter light and reduce contrast. The most common specification standard is MIL-PRF-13830B, which assigns a scratch-dig number (like 60-40 or 20-10) where lower numbers mean fewer and smaller defects. The right spec depends on where the surface is in the optical system — surfaces near a focal plane are more sensitive.
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Surface texture (surface roughness at the micro scale) describes the fine-scale irregularities left by the polishing process. Unlike surface form (which captures the large-scale shape error), texture operates at spatial frequencies that scatter light at wide angles. It’s typically specified as an RMS roughness value in nanometers or angstroms.
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After a lens element is coated, the coating’s reflectance and transmittance must be verified across the specified wavelength range. Spectrophotometers measure these properties, confirming that the coating meets the design specification for each wavelength and angle of incidence. Environmental testing (humidity, adhesion, abrasion) may also be required depending on the application.
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Before diving into test methods, it helps to understand what resolution means optically. The Rayleigh criterion and Dawes’ limit are ways to quantify resolution. They apply to both linear and angular resolution.
You’ve completed your lens, from design to prototyping to assembly. Now comes the moment of truth — how well does it perform? This page compares the major approaches to testing resolution, weighing accuracy, precision, speed, and cost.
The simplest and most intuitive way to evaluate a lens: image a standardized chart and see how fine a detail you can resolve. This page covers the method, its strengths (cheap, fast, visual), and its limitations (subjective, no contrast data).
MTF testing is the gold standard for verifying that a manufactured lens meets its design specifications. It captures contrast at every spatial frequency, giving you the most complete quantitative picture of lens performance.
The focal length of a lens determines its image size, so verifying it on a manufactured assembly is essential. Focal length is typically measured on an optical bench using a nodal slide or by imaging a target at a known distance. For multi-element designs, the effective focal length may differ slightly from the design value due to manufacturing tolerances.
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Distortion testing measures how well a manufactured lens matches its intended mapping function, whether that’s f·tan(θ), f·θ, or stereoscopic. Our page on distortion covers the theory behind each type and which is best for your application.
Aberration testing reveals the residual optical errors in an assembled system — invaluable for diagnosing manufacturing problems. Our page on optical aberrations covers the types (chromatic, spherical, coma, astigmatism, field curvature) and how they’re measured.
Interferometry is the most precise method for measuring wavefront error in an optical system. By comparing the wavefront produced by the lens under test to a perfect reference wavefront, an interferometer generates a fringe pattern that reveals the type and magnitude of aberrations present. Results are typically reported as a wavefront error map in fractions of a wavelength.
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The point spread function (PSF) describes how a lens images a single point of light. In a perfect lens, the PSF is an Airy pattern — a bright central disk surrounded by faint rings. In practice, aberrations distort this pattern in characteristic ways: coma produces a comet-like tail, spherical aberration creates a halo, and astigmatism elongates the disk. The star test is a simple visual version of PSF evaluation using a pinhole or distant point source.
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A Shack-Hartmann wavefront sensor uses an array of small lenslets to sample the wavefront across the aperture. Each lenslet focuses its portion of the wavefront onto a detector, and the displacement of each spot from its ideal position reveals the local wavefront slope. The full wavefront is then reconstructed from these slope measurements. This method is fast, robust, and works well for testing both optical systems and individual elements.
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The Strehl ratio is a single number that summarizes how close a lens is to diffraction-limited performance. It’s defined as the peak intensity of the actual PSF divided by the peak intensity of a perfect PSF. A Strehl ratio of 1.0 means the lens is perfect; a ratio above 0.8 is generally considered “diffraction-limited” for most practical purposes. It’s a useful shorthand when comparing optical systems or evaluating manufacturing quality.
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Illumination design determines how light is collected, transferred, and distributed through an optical system. Getting it right is critical in applications like scatterometers, projectors, and machine vision illuminators, where the quality and uniformity of the light source directly affects measurement accuracy or image quality. The key concept here is étendue — the fundamental limit on how much light an optical system can move — along with how stops and pupils control illumination uniformity.
The concept of étendue starts with the idea that it is really hard to stuff a lot of light into a small hole. Étendue is the number that tells you how big the hole is. More precisely, it’s the product of emitting area and solid angle, and because it’s conserved, it sets a hard limit on what any optical system can do with light. This page builds the concept from first principles with worked examples.
Stops and pupils appear here as well as in the Optical Design section because they play a distinct role in illumination: controlling how much light reaches the target and how uniformly it’s distributed.
There are two classical approaches to illumination design: critical and Köhler. In critical illumination, the light source is imaged directly onto the sample. It is simple but sensitive to source non-uniformity. Köhler illumination images the source onto the aperture stop instead, producing highly uniform illumination at the sample plane even if the source itself is uneven. Köhler illumination is the standard in projection systems.
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Radiometry measures electromagnetic radiation in physical units (watts), while photometry weights those measurements by the human eye’s sensitivity (lumens). The terminology can be confusing because each radiometric quantity has a photometric counterpart: radiant flux becomes luminous flux, irradiance becomes illuminance, and radiance becomes luminance. Understanding the distinction matters when you’re designing for a detector (use radiometry) versus designing for human vision (use photometry).
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When light hits a rough or translucent surface, it scatters. Measuring and understanding that scatter using instruments like scatterometers is essential for applications from AR/VR display testing to stray light analysis in imaging systems. Eckhardt Optics has deep expertise in scatterometry — we design and build scatterometers — and these pages cover the fundamentals of optical scattering, surface roughness measurement, and how scatter relates to roughness.
Our technical hub for engineers working with optical scatter and surface roughness. Covers conoscopic scatterometers, optical scattering theory, and practical measurement guides — including setup and use of instruments like the Mitutoyo SJ-210 stylus profiler.
There are two classes of instruments for measuring surface roughness: mechanical (stylus profilers) and optical. Mechanical instruments are cheaper. Optical instruments image an area of the surface, so you get more information. This page compares both approaches.
Specifying surface roughness correctly on a drawing or purchase order is critical — an incomplete or ambiguous spec can lead to parts that scatter too much light or cost more than necessary. This page covers the key parameters (Ra, Rq, PSD) and how to communicate your requirements clearly to a manufacturer.
Surface roughness and optical scatter are related but not the same thing. This page explains how roughness statistics map to BSDF measurements, and why that relationship matters when you’re predicting stray light performance from surface specifications.