**Modulation Transfer Function (MTF)**

The MTF of an optical system describes how the image contrast varies with spatial frequency. It is expressed as the ratio of contrast in the image to contrast in the object as a function of spatial frequency. There are multiple ways to measure MTF–in the simplest form, a series of patterns with known spatial frequencies would be placed at the object plane, and the contrast in the image plane would be measured. This method produces discrete data points, and would make sense if there were only a very small number of object patterns necessary to cover all testing needs for all lenses.

This is usually not the case, and the process of changing patterns would be cumbersome and time consuming. A preferred technique is to make use of a simple geometric target such as a circular aperture (loosely referred to as a pinhole) or a slit aperture. Fourier analysis shows that these geometries may be generated by summing an infinite series of sinusoidal patterns, so that by obtaining the inverse Fourier transform of the image formed by a lens when presented with these optical “impulses” we can measure the spatial frequency response of the lens under test at all frequencies simultaneously.

Compared with other forms of optical testing, MTF measurement is the most direct and accurate measure of system performance, producing a far more accurate account of the performance of a lens or optical system over its full spatial frequency range. Among the inherent advantages that MTF measurement has over other forms of optical testing:

– It is an objective test of the imaging quality of an optical system that does not rely on operator judgment

– It allows for testing in real-world situations, including off-axis configurations and polychromatic illumination

– It can be directly compared to design specifications and theoretical evaluations

The MTF of an optical system can measured at multiple points across the field of view of the lens The standard set of field points measured by the Optikos IQ Lab™ includes measurements on axis, at ± 50% of the full field, and at ± full field. Our MTF report provides tangential and sagittal MTF values at those five field points, as shown in the sample report below.

Interested in MTF testing? Here’s what we need from you:

– Entrance pupil diameter

– Effective focal length

– Full Field of View

– Desired Test Spectrum

– Spatial Frequencies of interest (if any)

Please request a quote through our IQ Lab Testing Questionnaire.

**Effective Focal Length (EFL)**

Focal length is a commonly specified parameter of a lens, and is defined as the inverse of the optical power of the lens. The terms “focal length” and “effective focal length” are mostly used interchangeably – use of the term “effective focal length” avoids confusion with other related parameters, like Back Focal Length (BFL) or Flange Focal Length (FFL).

When a lens is operating at infinite conjugates, the EFL relates the angle at which light from the distant object is incident on the lens (θ) to the corresponding height where the light comes to a focus in the image plane (h). The ideal relationship is described by:

h=EFL*tanθ

This relationship can be used to calculate the paraxial EFL by measuring the object angle and the image height for the lens under test. The lens under test is rotated so that the collimated object beam is incident on the entrance pupil at a known angle, and the resulting height of the image is measured by our OpTest 7 software and used to calculate the EFL of the lens. The object beam angle is selected to be less than 1/10th of the field of view of the lens under test, so as to ensure that the measurement is not affected by the presence of geometric distortion.

The standard Optikos IQ Lab EFL measurement consists of performing the measurement described above 10 times in a row. As shown in the sample report below, the data report provides the 10 measured values, the calculated average EFL value, and statistical information about the collected data set.

Interested in EFL testing? Here’s what we need from you:

Nominal entrance pupil diameter/f-number

Nominal effective focal length

Full field of view (specified in object angle or image plane height)

Desired Test Spectrum

Spatial Frequencies of interest (if any)

See our Standard Measurement Price List for typical EFL measurement pricing for catalog lenses. For your custom testing needs, please request a quote through our IQ Lab Testing Questionnaire or contact the IQ Lab department at IQLab@optikos.com or 617-902-3151.

**Distortion**

Distortion is a measure of the change in focal length with field angle. When distortion is present, the following relationship between the object beam angle (θ) and the corresponding image height (h) is no longer true across the field of view of the lens:

h=EFL*tanθ

To measure distortion, the lens under test is rotated through successive angles and the resulting image height is measured at each point. The measured image height (hmeasured) is compared to the theoretical image height (hideal) using the equation:

% Distortion=100 ×(h_measured-h_ideal)/h_ideal

The standard distortion measurement, as performed by Optikos IQ Lab™ services, consists of measuring the image centroid at 10 field points across the field of view of the lens under test. Our standard distortion data report is shown below.

Interested in distortion testing? Here’s what we need from you:

Nominal effective focal length

Full field of view

Desired Test Spectrum

Spatial Frequencies of interest (if any)

See our Standard Measurement Price List for typical distortion measurement pricing for catalog lenses. For your custom testing needs, please request a quote through our IQ Lab Testing Questionnaire or contact the IQ Lab department at IQLab@optikos.com or 617-902-3151.

**Field Curvature**

The term “image plane” is used to describe the imaginary surface on which the best focused image falls over the field of view of the lens. It is seldom a true plane, and knowing the departure from true planarity is often a metric of interest in quality control. Additionally, it is usually expected that the image plane (or the best fit plane to a curved image plane) will be perpendicular to the optical axis of the lens, or to a mechanical axis. Any departure from the perpendicular condition is referred to as field tilt.

The measurement method that the Optikos IQ Lab™ employs is to find the Z-axis location of the best focus position for the image at each specified field point. These are graphed as a set of best focus displacements from the best on-axis focus position. Additionally, a best-fit straight line is found, the slope of which is reported as field tilt.

The standard set of field points used by the Optikos IQ Lab™ services to measure field curvature includes on axis, ± 50% of the full field, and ± 100% of the full field. As shown below, our field curvature report provides the location of the best focus at those five field points, and reports astigmatism and field tilt values.

Interested in field curvature testing? Here’s what we need from you:

– Nominal entrance pupil diameter/f-number

– Nominal effective focal length

– Full Field of View (specified in object angle or image plane height)

– Desired Test Spectrum

– Spatial Frequencies of interest (if any)

**Chief Ray Angle**

A chief ray is the ray from an off-axis object point which passes through the center of the aperture stop of an optical system. The chief ray enters the optical system along a line directed towards the midpoint of the entrance pupil, and leaves the system along a line passing through the center of the exit pupil. To measure the angle between the optical axis and the chief ray on the image side the following method is used: The lens under test is illuminated by the collimator at different angles corresponding to the object sided chief ray angles. The detector head is moved to the image field position at which the lens focuses the image. Now the detector head is moved towards the lens in small steps while the software registers the lateral movement of the focused spot. From these lateral movements the CRA is calculated. At Optikos, chief ray angle (CRA) is measured by our OpTest^{® }MTF Testing System and LensCheck™ VIS.

See our Standard Measurement Price List for typical field curvature measurement pricing for catalog lenses. For your custom testing needs, please request a quote through our IQ Lab Testing Questionnaire or contact the IQ Lab department at IQLab@optikos.com or 617-902-3151.