Mtf measurementchart

To be able to choose the right Focal Length lens for a specific camera model with corresponding sensor size two measurements will need to be taken; distance to target scene (or shot) and width of scene (or shot) to be captured by camera at that distance. Then plugging these data points into a FOV calculator or app will provide a Focal Length on given sensor size. For instance, a 1/3” camera sensor at a 10 foot distance needing to capture a 15’ horizontal shot (16:9 HD ratio) would require a 3.6mm focal length (image from pCAM Pro app from iPhone shown here).

For a deeper analysis, WaveView4 can also compute the Point Spread Function (PSF), wavefront aberrations and Zernike or Legendre polynomials.

Mtf measurementpdf

Choosing the right lens can seem complicated when designing for a desired camera position, shot, or perspective. Zoom cameras take out some of the guesswork, however even these cameras have a minimum and a maximum focal range. Then add in differences between parfocal and varifocal zoom lenses, further complicates the mission and might not be relevant to project scope.

Modulation transfer function Radiology

Note that the HASO R-FLEX instrument can also be used to  characterize large optics if combined with the LA ( Large Aperture ) accessory module.

Fixed Prime vs Varifocal lenses offer different perspectives even if the Focal Length in the Varifocal (variable focal length) lens is set to match the Fixed Focal Length Prime lens. When a Varifocal lens is used, different settings within the variable focal range effect Depth-of-Field (DOF). Fixed Prime lenses will hold everything within the FOV in focus or might be stated as “near contact to infinity in focus”.

MTFimage quality

The Modulation Transfer Function or MTF measurement is a crucial metrology technique to evaluate how an object’s contrast is captured after passing through an optical system as a function of spatial frequency. It is a critical criteria especially for imaging systems, as it quantifies the imaging quality. The MTF curve is usually compared to the ideal MTF given by a diffraction limited optical system (see Figure 1).

Not to complicate further but given same fixed Focal Length; a larger sensor size will widen the AOV and smaller sensor size the more narrow.  This creates a challenge to match say a DSLR focal length look with a corresponding AOV in a miniature or smaller camera sensor.  For instance, a 35mm lens on a DSLR camera is a relatively wide AOV perspective, however on a 1/3” or 1/2” sensor it is more of a telephoto or narrow AOV perspective.

In this article we present a MTF measurement performed with a HASO SWIR Shack-Hartmann wavefront sensor manufactured by Imagine Optic SA, a company renowned for its expertise in optical metrology instrumentation for over 25 years. It is combined with the RFLEX accessory which combines a light source and allows an easy double pass set-up.

Mtf measurementformula

On the screenshot below, we can clearly see that this optical system on Figure 2 has aberrations. Indeed, the wavefront is not uniform and the MTF curve (solid line) is not close to the diffraction limit (dotted line).

Field-of-View (FOV) and Angle-of-View (AOV) vary slightly because FOV considers entire field including Depth-of-Field (DOF) or minimum distance from camera lens in-focus to farthest distance in-focus where nearer or farther are out-of-focus.  AOV is an angle from glass extending outward as an angle in degrees (ie. 85°, 100°) essentially different angles from glass to infinity extending outward.

Modulation transfer function

The MTF measurement can be processed from the wavefront map using a double fourier transform. Shack-Hartmann sensors provide the wavefront map in just in a single shot acquisition and therefore provide almost instantaneously a 2D-MTF measurement, offering access to every azimuthal angle.

Then it’s as easy as matching that Focal Length (mm) to an appropriate lens model as a Fixed Prime lens or Varifocal lens that falls within the range. For example, a 2.8~12mm will cover the 3.6mm requirement with lots of flexibility to adjust.

As the MTF is a quantitative and standardized way to characterize optical systems, MTF measurements are commonly used by optical engineers and designers in order to:

HASO sensor offer a measurement accuracy of  λ/100 rms which translates to a MTF calculation with an accuracy of less than 1 point (1%). Moreover, this measurement solution allows convenient implementation allowing on-axis and off-axis measurements.

In generally terms; Focal Length (mm) describes distance between rear lens elements and sensor in digital cameras. Depending on size of sensor a given Focal Length (mm) lens will capture a specific angle-of-view (AOV) in degrees. The higher the numerical Focal Length in mm the longer or more-narrow the shot becomes, these longer focal length lenses are considered telephoto, given same sensor size. Likewise, the lower the Focal Length in mm, same sensor size, the wider the shot becomes capturing a wider AOV perspective of the scene.