1. Sensor Size from Pixel Pitch and Resolution

In electro-optical and infrared imaging systems, sensor width and height should not be guessed only from commercial format names. They can be calculated from detector resolution and pixel pitch.

For example, a 640 × 512 detector with 12 µm pixel pitch has a sensor width of 7.68 mm and a sensor height of 6.14 mm.

2. Required Image Circle

The minimum image circle required to cover a sensor is determined by the sensor diagonal. This value comes from the sensor geometry, not from the lens.

A lens should provide an image circle larger than the sensor diagonal. For safe engineering use, a margin can be added. In our calculator, a 0.5 mm safety margin is used.

3. Lens Image Circle

The actual lens image circle is not calculated from the sensor. It is a lens design or datasheet parameter. It depends on the optical design, mechanical aperture, vignetting, relative illumination, MTF limit and accepted image quality at the field edge.

4. Coverage, Vignetting and Crop

If the lens image circle is smaller than the safe required image circle, the full sensor area may not be safely usable. In that case, vignetting may occur, or a cropped active sensor area may be required.

If the image circle is smaller than the sensor diagonal, the corners may be outside the usable optical field. If the image circle is slightly larger than the diagonal but has insufficient safety margin, the result should be treated as borderline.

5. Field of View

Field of view is calculated from sensor size and focal length. Horizontal, vertical and diagonal FOV should be evaluated separately, especially when sensor aspect ratio differs from common photography formats.

6. Distortion

Distortion does not define the image circle itself. However, it affects the geometric accuracy of the field of view and the mapping between object space and image space. For low-distortion lenses, the ideal FOV formula is usually sufficient. For wide-angle or high-distortion optics, distortion should be considered separately as a correction factor.

1. What is F-number?

F-number, also written as F/#, describes the relationship between the focal length of a lens and the effective aperture diameter. It is one of the most important parameters in optical design because it affects light collection, depth of field, diffraction, exposure and optical system size.

For example, a 50 mm lens with a 25 mm entrance pupil has an F-number of F/2. A 50 mm lens with a 50 mm entrance pupil has an F-number of F/1. Lower F-number means a larger aperture and higher light collection capability.

2. Aperture Diameter

If focal length and F-number are known, the effective aperture diameter can be estimated directly. This is especially useful when evaluating lens size, optical throughput and mechanical feasibility.

A 100 mm F/2 lens requires approximately a 50 mm entrance pupil. A 100 mm F/1 lens requires approximately a 100 mm entrance pupil. This is why fast long-focal-length optics become physically large and mechanically more demanding.

3. Light Collection and F-number

Light collection is not proportional to F-number directly. It is proportional to the aperture area. Because aperture diameter changes with F-number, the amount of collected light changes approximately with the square of the F-number ratio.

For example, an F/1.0 optical system collects approximately four times more light than an F/2.0 system, assuming similar transmission and detector conditions. This is highly important for LWIR, MWIR, SWIR, low-light visible imaging and laser spot observation systems.

4. F-number in EO/IR Systems

In electro-optical and infrared systems, F-number strongly affects sensitivity and detection performance. A lower F-number allows more energy to reach the detector, which can improve signal level and low-contrast target visibility. However, very fast optics are harder to design, manufacture, align and package.

For thermal cameras, F-number also influences the amount of infrared radiation reaching the detector. Low F-number LWIR lenses can improve thermal signal strength, but they may require larger germanium optics, tighter tolerances and more careful control of aberrations.

5. Trade-off: Fast Optics vs Image Quality

A lower F-number is not automatically better. Fast lenses may have stronger aberrations, tighter tolerance requirements, larger lens diameters and higher cost. The final choice must balance light collection, resolution, field of view, detector size, mechanical envelope, environmental robustness and manufacturability.

6. Practical Engineering Note

When selecting a lens for an EO/IR system, F-number should be evaluated together with focal length, detector pixel pitch, sensor format, image circle, MTF, transmission, wavelength band and environmental operating conditions. A lens that looks attractive only by F-number may not be suitable if it cannot deliver sufficient image quality across the required field.

1. What is Diffraction?

Diffraction is a fundamental wave-optics effect that occurs when light passes through an aperture. Even a perfect lens cannot focus light into an infinitely small point. Instead, the focused spot has a finite size known as the diffraction pattern.

The central bright region of this diffraction pattern is called the Airy disk. In high-quality optical systems, the Airy disk can become one of the main limits of resolution.

2. Airy Disk Diameter

The approximate diameter of the Airy disk at the image plane depends on wavelength and F-number. This relationship is extremely important when comparing optical spot size with detector pixel pitch.

In this formula, wavelength and Airy disk diameter must use the same unit. If wavelength is in micrometers, the Airy disk diameter will also be in micrometers.

3. Example: Visible, SWIR and LWIR

Diffraction becomes more significant at longer wavelengths. This is why LWIR systems are much more diffraction-sensitive than visible systems for the same F-number.

This shows why a lens that is excellent for visible imaging may not behave the same way in LWIR. Wavelength directly changes the diffraction-limited spot size.

4. Diffraction vs Pixel Pitch

A practical way to evaluate diffraction is to compare the Airy disk diameter with the detector pixel pitch. If the Airy disk is much smaller than the pixel pitch, the detector may limit the resolution. If the Airy disk is similar to or larger than the pixel pitch, diffraction becomes a major contributor to image blur.

For example, in a LWIR camera with 12 µm pixel pitch and an F/1.0 lens at 10 µm wavelength, the Airy disk diameter is approximately 24.4 µm. This is about two pixels wide, meaning diffraction is already an important part of the system resolution.

5. Diffraction-Limited vs Real Lens Performance

A diffraction-limited lens is a lens whose performance is mainly limited by diffraction rather than by aberrations or manufacturing errors. However, many real optical systems are not perfectly diffraction-limited, especially at wide field angles, low F-number or broad wavelength bands.

Real performance also depends on spherical aberration, coma, astigmatism, field curvature, chromatic effects, coating performance, alignment, focus error, temperature effects and mechanical tolerances.

6. MTF and Resolution

Modulation Transfer Function, or MTF, is commonly used to describe how well an optical system transfers contrast at different spatial frequencies. Even if the theoretical diffraction limit looks acceptable, the actual lens must still provide sufficient MTF at the detector sampling frequency.

If pixel pitch is 12 µm, the detector Nyquist frequency is approximately 41.7 lp/mm. The optical system should be evaluated at or near this spatial frequency to understand whether the lens can properly support the detector resolution.

7. Practical Engineering Note

Diffraction should always be considered together with pixel pitch, wavelength band, F-number and MTF. For visible systems, small pixels may be meaningful because diffraction spots are relatively small. For LWIR systems, the longer wavelength makes diffraction much more dominant, so simply reducing pixel pitch does not always improve real image detail unless the optics can support it.

1. What does MTF tell us?

Modulation Transfer Function, or MTF, describes how much contrast an optical system can transfer from the object to the image at different spatial frequencies. Low spatial frequencies represent large structures and general image contrast. High spatial frequencies represent fine details, edges and small target features.

In optical design, MTF must be evaluated together with wavelength band, field position, F-number, focal length, sensor format, pixel pitch and required application performance.

2. Which spatial frequency should be used during optical design?

A practical starting point is the detector Nyquist frequency. The Nyquist frequency is the highest spatial frequency that the detector can sample without aliasing, based on pixel pitch.

Pixel pitch must be used in millimeters if the result is desired in line pairs per millimeter.

Therefore, for a 12 µm detector, checking lens MTF around 40 lp/mm is highly meaningful. For a 5 µm detector, the Nyquist frequency becomes 100 lp/mm, and the optical design must support much higher spatial frequency if the small pixel size is to be fully useful.

3. When can we say “this MTF is sufficient”?

There is no universal single MTF number that is valid for every optical system. The acceptance threshold depends on the mission. However, a useful engineering approach is to evaluate MTF at the detector Nyquist frequency and also at half-Nyquist frequency.

As a practical rule, if the lens keeps acceptable contrast at the detector Nyquist frequency across the required field and wavelength band, the design is generally well matched to the detector. If MTF is strong only at low frequency but collapses near Nyquist, the system may produce acceptable-looking images but will not fully use the detector resolution.

4. Lens MTF alone is not the final system MTF

When the lens is mounted on a real sensor, the final image quality is not determined by lens MTF alone. The sensor also has its own sampling behavior. Pixel aperture, fill factor, detector diffusion, electronics, focus error, alignment and image processing can reduce final system contrast.

This means a lens with high theoretical MTF may still produce lower real image sharpness if the detector sampling, focus, alignment or processing chain is not well controlled.

5. Detector MTF and pixel aperture effect

A detector pixel is not an ideal point sampler. It has a finite active area. Because of this, the detector itself reduces contrast at high spatial frequencies. A simplified one-dimensional pixel aperture MTF can be represented by a sinc function.

Here, f is spatial frequency in lp/mm and p is pixel pitch in mm. This simplified formula shows why high-frequency detail becomes harder to preserve as spatial frequency approaches Nyquist.

6. How to decide if lens + sensor MTF is sufficient?

The correct approach is to evaluate the combined system MTF at the spatial frequency relevant to the detector. In practice, this means checking the lens MTF at the detector Nyquist frequency, estimating detector MTF, and multiplying them to estimate system-level contrast transfer.

7. Practical example

Assume a detector has 12 µm pixel pitch. Its Nyquist frequency is approximately 41.7 lp/mm. If the lens MTF at 41.7 lp/mm is 0.45 and detector MTF at the same frequency is approximately 0.64, the estimated system MTF becomes:

This means that although the lens alone transfers 45% contrast at Nyquist, the combined lens-sensor system may transfer approximately 29% contrast at that spatial frequency. This is why lens MTF must be interpreted together with detector sampling.

8. Design acceptance logic

During optical design, the lens should not be evaluated only by its best on-axis MTF. The decision should be made according to the worst acceptable field position and application need.

9. Optical Design MTF vs Measured Final System MTF

Optical design MTF and measured final system MTF must be interpreted separately. Optical design MTF is obtained from software such as Zemax, Code V or OpticStudio. It represents the predicted lens performance under selected design assumptions such as wavelength, field position, F-number, focus condition and tolerance state.

During design review, the relevant MTF values should not be taken only from the best on-axis curve. A conservative decision should use the weakest relevant field position, the lower sagittal or tangential curve, and the tolerance degraded result whenever tolerance data are available. This gives a more realistic view of whether the optical design can support the selected detector.

10. Final Measured System MTF and OK/NOK Decision

Measured final system MTF is different from lens design MTF. It is obtained after the real lens, detector, mechanics, electronics and image processing chain are assembled and tested. A collimator, slanted-edge target, bar target or equivalent optical test setup may be used to obtain the measured system MTF.

For a final product, OK/NOK acceptance should ideally be based on the product specification. If the technical specification defines minimum measured system MTF values at 0.5 × Nyquist and Nyquist, those limits should be used as the formal acceptance criteria.

Therefore, measured system MTF should not be multiplied again by detector MTF. It already represents the real integrated lens-detector system performance. If the optical design MTF is acceptable but measured system MTF is weak, the issue may come from focus, alignment, assembly, detector sampling, processing, electronics or test setup.