Optical Resolution & MFOV

The optical resolution is a crucial specification parameter for temperature measurement, indicating the ability to resolve an object with sufficient accuracy. A small field of view of a measuring device is associated with a small measuring spot size and a higher optical resolution of the target.

From a technical point of view, optical resolution is linked to the optical system of the measurement device and the detector size for a pyrometer or the sensor’s pixel size for a thermography camera. Both together define the optical resolution for the temperature measurement application. This definition accounts for the optics’ spherical and chromatic aberrations, the detector’s effective area, and the scattering effects within the optical system.

Several interrelated factors in the optical and detector system fundamentally limit the optical resolution of any optical sensor. The main limitations are diffraction set by wavelength, lens quality, and detector size, collectively limiting the optical resolution of an infrared sensor.

The quality of the lenses and their design determine how precisely the system can focus infrared radiation onto the detector. Optical aberrations, diffraction effects, and imperfect focusing reduce the system’s ability to distinguish small details, especially at long distances.

The detector typically measures radiation from a single spot. The smaller the detector, the finer the spot it can resolve — but only if the optics are also capable of projecting such a small spot. This is finally limited by diffraction.

When infrared light passes through a lens, it forms a diffraction-limited spot Airy disk rather than a perfect point. The point spread function describes this blurred intensity distribution at the image plane. Figure 1 illustrates how a point source is broadened due to diffraction, spreading its energy across adjacent pixels.

According to the Rayleigh criterion, two-point sources are just resolvable when the maximum of one Airy disk coincides with the first minimum of the other. The minimum resolvable feature size [math]∆l_{min}[/math] is defined in the following equation, where [math]\lambda[/math] is the infrared wavelength, f is the lens’s focal length, and [math]D[/math] is its diameter. This value also defines the radius of the Airy disk:

[math]∆l_{min}=1.22 (f \cdot λ )/D[/math]

The optical resolution of the system is the reciprocal of ∆lmin. This diffraction limit defines the ultimate resolution regardless of sensor size or pixel pitch. The optical resolution of an optical system is generally defined as the reciprocal of the mentioned equation 1/[math]∆l_{min}[/math]. The aperture diameter [math]D[/math] plays a critical role in determining the diffraction limit — smaller apertures produce wider Airy disks and thus lower spatial resolution.

The following equation describes the shape of the airy disk:

[math]I\left(x\right)=\ \frac{2\ J_1(\alpha)}{\alpha}[/math]

[math]\alpha=\ \frac{2\pi}{\lambda}\ \cdot \ \frac{ax}{z}[/math]

Whereas [math]\ J_1[/math] is the first-order Bessel function, a is the aperture radius, and [math]z[/math] is the distance from the aperture to the image plane. This is the standard normalized Airy disk profile, assuming peak intensity at the center is to be defined 1.

Due to diffraction, the minimum resolvable spot size is directly proportional to the wavelength of the infrared light used. Longer wavelengths (e.g., 8–14 µm) result in larger diffraction-limited spot sizes compared to shorter wavelengths (e.g., 1–2 µm). Thus, infrared thermal sensors operating in the shortwave IR range inherently offer better optical resolution.

If the detector element is significantly larger than the wavelength, the detector size primarily defines the optical resolution. However, when the detector dimensions approach the scale of the wavelength being measured, diffraction effects become relevant and impose optical limitations. In contrast to pyrometers, which rely on a single detector to measure infrared radiation, infrared cameras employ two-dimensional focal plane arrays to capture thermal images. The pixel size of these arrays is often comparable to the infrared wavelength, resulting in a fundamental diffraction limit that restricts the achievable spatial resolution.

The term measurement field of view MFOV is derived from these theoretical considerations. Whereas the instantaneous field of view (IFOV) defines the smallest spatial detail the camera can theoretically resolve at a given distance, assuming perfect optics, the minimum field of view (MFOV) represents the necessary target object size that needs to be covered by a defined number of pixels for accurate temperature measurements.

The following figures illustrate that, with the same optical system, a higher pixel density does not improve image quality as the infrared energy is distributed across an area. Therefore, for a small pixel pitch, a larger number of pixels must be measured to ensure accurate temperature measurement.  If the pixel is larger than the airy disc, then it is sufficient to measure only an individual pixel.

In pyrometry, the distance-to-spot size ratio is typically defined as the blackbody diameter at which the measured radiation signal decreases by 10% compared to the signal from a sufficiently large blackbody. For infrared cameras, this concept can be transferred by using the image size at which 90% of the total energy is encircled to define the effective measurement field of view. This value directly relates to the number of pixels needed to fully capture the focused infrared spot. Suppose the image size falls below this 90% energy diameter. In that case, the collected energy per pixel drops significantly, leading conventional infrared cameras, which rely on pixel-based intensity measurements, to underestimate the actual temperature. Figure 4 shows the experimental data, with the corresponding 90% encircled energy sizes listed in Table 1. In these measurements, performed at a blackbody temperature of 100 °C, a ~10% reduction in collected energy results in a temperature deviation of approximately 7.2 °C. The deviation is most pronounced for cameras with smaller pixel pitches. While smaller object features may still be detected, the minimum reliable feature size for accurate temperature measurement is primarily determined by the optical diffraction limit of the infrared system, rather than by the pixel size alone.

In summary, from a physical point of view, the diffraction-limited properties of the optical system are a natural limitation on optical resolution and image quality, even with higher pixel number and smaller pixel size. Since the dimensions of the individual pixels are already similar to the wavelength being detected, the resolution of the optical system is limited.

In the long-wavelength infrared range, with pixel pitch of 17µm, it is generally required that the target object spans at least three pixels, corresponding to three times the IFOV, to ensure that 90% of the emitted radiation is captured and the distance ratio is reliably defined. If the pixel pitch is smaller than 12 µm, more pixels must be considered for a correct temperature reading.  with lower quality optical systems, in some circumstances as many as 10×10 pixels may be required to receive 90% of the energy. A high-performance camera lens also allows for a larger measuring distance with the same number of pixels on the detector, or for the precise temperature measurement of smaller structures and objects.

Abbe limit for microscopes

For microscopic or high-magnification infrared imaging, the resolution is often described in terms of the Abbe limit. This approach introduces the concept of the numerical aperture, which measures the range of angles over which light can enter or exit the optical system. Especially for microscopic applications, the Abbe resolution limit is often referenced. Here, the Abbe definition is very close to the presented equation, but considers the numerical aperture  instead of the f-number, resulting in the smallest size of a resolvable object d. The system’s numerical aperture (NA) measures the angles over which light can enter or exit the system. Both terms are related to each other. Unlike the f-number, the numerical aperture considers the refractive index n of the medium in which the system works.

[math]d=\ \frac{\lambda\ }{2n\ \cdot \ \sin{(\varphi)}}=\ \frac{\lambda\ }{2NA}[/math]