Due to the easy system conversion from VIS to NIR, the specific requirements from various areas, including the automotive industry, development of mobile phone lenses, and the military and aerospace sectors are covered.

Usually the MTF is used in its one-dimensional form, calculated for one azimuthal section through the image plane. The azimuth (section plane) of the object pattern is called sagittal azimuth when the prolongation of the slit or object passes through the reference axis. When the prolongation of the slit pattern is perpendicular to the reference axis, the azimuth is called tangential azimuth.

The ImageMaster® HR has been the MTF test station preferred by R&D laboratories worldwide and has always offered highest accuracy and repeatability. As the successor to the worldwide standard for image quality testing of lenses, the newly developed, ImageMaster® HR 2 is available, e.g. for smartphones, surveillance cameras and camera modules for the automotive industry.

The MTF measurement is an important tool for the objective assessment of the imaging performance of optical systems. Moreover, the MTF can be calculated from the lens design data giving designers of optical systems the ability to predict system performance reliably. The manufacturer can then compare the image quality of real lenses with the expectations from the design phase.

Relative illumination in an optical system is the gradual reduction of the image brightness with increased off-axis angle. This phenomenon results from the fall of, which is approximated by the cos4 or “cosine four law of the illumination falloff. Additionally there is the effect of the apparent limitation of the clear aperture depending on the field angle. Relative illumination is defined as the ratio of the central transmission and the transmission at the edge of the field of view.

Field curvature is an optical aberration in which the focus position changes from the center to the edge of the field of view. The curvature of the image field is a lens aberration that causes a flat object surface to be imaged onto a curved surface rather than a plane.

To determine the field curvature a set of through focus measurements at different positions in the field are taken. The MTF maxima and the corresponding positions in field are determined. The values are collected by a software routine and displayed in graphical and tabular form.

The Modulation Transfer Function (MTF), describing the resolution and performance of an optical system, is the ratio of relative image contrast divided by relative object contrast MTF = Relative Image Contrast/Relative Object Contrast. When an object (illuminated target or reticle) is observed with an optical system, the resulting image will be somewhat degraded due to inevitable aberrations and diffraction phenomena. In addition, a real lens will not fully conform to the design data.

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However, the EFL can be measured quickly and with sufficient accuracy using the method of measuring the magnification of a double bar target. Certified master lenses from PTB (National German Standard Institute) are available at TRIOPTICS and are used for the calibration of the measurement setup. The measurement data are thus directly traceable to international standards.

Due to the dispersion of refractive optical systems the image position and also magnification of an optical system depends on the wavelength of the light. The dependence of the axial image position on the wavelength is called Chromatic Focal Shift. The dependence of the magnification on the wavelength is called Lateral Chromatic Aberration. Both aberrations can be measured with the ImageMaster®. The collimator of the ImageMaster® is equipped with different narrow bandwidth color filters. Together with the highly corrected relay optics this enables the system to focus in axial direction to the different image positions for different colors. The image position measurement can be done with submicron accuracy. Measuring the lateral image position for different object angles enables the system to measure the lateral chromatic aberration.

The depth of focus is the extent of the region in front of and behind the image plane in which the image will appear to be sharp.

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The software offers high flexibility for measurements in the NUV-, VIS- and NIR spectrum. Automatic measurement sequences ensure easy operation and the data can be output in CSV/MHT.

The ImageMaster® HR 2 offers versatile functionality for testing the image quality of small and medium-sized lenses, e.g. for smartphone, photo and film cameras. With the ImageMaster® HR TempControl test samples, which have to provide their optical functionality and performance at extreme temperatures, can be measured in a wide temperature range.

TRIOPTICS provides customers maximum versatility offering a combined test system. The three exchangeable measurement heads offer the following possibilities:

• Motorized finite conjugate stage with manual or motorized object generator. The motorized object generator illuminates the reticle in the direction of the sample for off-axis measurements. This is needed for small samples or low light conditions • Various collimators with focal length and clear aperture for high flexibility • Motorized reticle and filter changer for infinite conjugate to measure with least interaction of an operator. The lateral chromatic aberration can be measured more accurately as the filter will be changed automatically with no vibration of a manual change • With the veiling glare upgrade for ImageMaster® HR it is possible to measure the Glare Spread Function (GSF). By off-axis measurements and rotation of the specimen around its center, the GSF can be measured over the entire field of view of the sample.

The measurement accuracy is traceable to international standards. The correlation to production testers and other devices enables worldwide consistent measurements independent of location as well as consistent measurement results in the product lifecycle from R&D to production.

Laser beams have certain common characteristics, but also vary to a wide degree with respect to size, divergence, and light distribution across the beam diameter. These characteristics depend strongly upon the design of the laser cavity (resonator), and the optical system controlling the beam, both within the cavity and upon output. Although a laser may appear to produce a uniform bright spot of light when projected onto a surface, if the light intensity is measured at different points within a cross section of the beam, it will be found to vary in intensity. Resonator design also affects beam divergence, a measure of beam spreading as distance from the laser increases. The beam divergence angle is an important factor in calculating the beam diameter at a given distance.

The ImageMaster® HR fulfils the high customer requirements for accuracy and flexibility in the measurement of image quality.

The ImageMaster®-Software measures continuously the light intensity of the test pattern in order to avoid saturation. In this way the necessary data is available for determining the relative illumination following ISO 13653:1996.

Many optical systems such as lenses and camera modules are used in a wide temperature range and must consistently maintain their full functionality and performance across varying temperatures. Athermal designs should minimize the thermal influences on opto-mechanical parameters.

For finite conjugate measurements a finite stage is available as upgrade in two different stage lengths for all wavelength ranges:

Modulation transfer function

where N is an integer, and λ is the wavelength. The condition for resonance is not as critical as it might appear because actual laser transitions in the cavity are distributed over a range of wavelengths, termed the gain bandwidth. Wavelengths of light are extremely small compared to the length of a typical laser cavity, and in general, a complete roundtrip path through the cavity will be equivalent to several hundred thousand wavelengths of the light being amplified. Resonance is possible at each integral wavelength increment (for example 200,000, 200,001, 200,002, etc.), and because the corresponding wavelengths are very close, they fall within the gain bandwidth of the laser. Figure 1 illustrates a typical example in which several resonance values of N, referred to as longitudinal modes of the laser, fit within the gain bandwidth.

A more complex measurement can be done simulating the range of object distances covered by the lens and measuring the MTF at the corresponding image distances.

Several useful functions are integrated which help the user to scan and perceive the correct image position of the sample under test. Changing the measurement mode is easy and time-saving. All important measurements for the imaging properties are quickly accessible.

The Effective Focal Length (EFL) or equivalent focal length is the distance from the focal points of the lens to the respective principal planes. The EFL determines the magnification of a lens and hence the image size. Because the principal planes are usually inside the lens at unknown locations, the direct measurement of the EFL is difficult.

The tutorial initializes with the gain bandwidth and cavity frequency set at values of 1.5 gigahertz and 476 terahertz, respectively. In order to operate the tutorial, use the mouse cursor to translate the Gain Bandwidth frequency slider between the ranges of 1 and 2 gigahertz. As this slider is translated, the yellow bandwidth curve changes shape to accommodate the new frequency range. The number of cavity modes can be adjusted with the Cavity Frequency slider, which simultaneously varies the modes drawn with red curves in the tutorial window.

FOV and focal length

All MTF measurements can be performed with the ImageMaster® Universal in finite, infinite and afocal measurement position.

Powerful functions assist the user in performing the necessary measurement processes to determine a variety of parameters to determine the optical performance in the extended temperature range.

Distortion is the percentage of change in magnification between the center of the field of view and off-axis positions in the field of view. In order to determine the distortion a different method of measuring the EFL is used:

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The Modulation Transfer Function (MTF) is an important aid to objective evaluation of the image-forming capability of optical systems. Not only that the MTF provides a means of expressing the imaging quality of optical systems objectively and quantitatively, but it can be calculated from the lens design data. In this way it allows optical and systems designers to predict reliably the performance of the optical systems. The manufacturers can compare the image quality of the manufactured lenses with the design expectations.

One main feature key feature when using the software with the ImageMaster® Universal is the support of UV or IR detectors employing the scanning aperture method.

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Innovative design, high quality and long-life components are combined in the ImageMaster® Universal with user-friendly software. Its horizontal construction facilitates testing of large lenses.

In general, the image quality of lenses can be affected by temperature influences on the optical components and mounting materials. Crucial lens parameters such as effective focal length and flange focal length can be temperature-dependent and have an impact on the camera’s focusing function.

Hence this type of polarization is called circular polarization. d. Elliptical polarization. All of the states of polarization described above are actually ...

The devices ImageMaster® HR 2 and Universal provide an outstanding level of accuracy and flexibility when testing the MTF (modulation transfer function). The equipment is modular and upgradeable to allow for custom configuration as test requirements change. The instrument can be configured for testing optical systems with the object at infinity or object and image at finite conjugates. The accuracy of the measurement is traceable to international standards.

Jul 14, 2021 — Yes. It should technically be read as "Electromagnetic waves will interfere with others if their direction of polarization is not perpendicular" ...

MTF testingMastercard

The products ImageMaster® HR 2 and Universal fulfill highest customer requirements for image quality testing. ImageMaster® HR 2 is the preferred MTF test station for R&D labs worldwide. Measurements with increased accuracy and flexibility are the main focus.

In a typical laser, the number of cavity resonances that can fit within the gain bandwidth is often plotted as a function of laser output power versus wavelength. This interactive tutorial explores how varying the appropriate frequencies can alter curves describing the number of cavity modes and gain bandwidth of a laser.

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ImageJMTF

The F-Number of a lens is defined by the ratio between the EFL and the diameter of the entrance pupil. The ImageMaster® series instruments use the ISO-517 method to accomplish the measurement: First the EFL is measured according to the procedure described before. Then the sample is turned around with the entrance pupil facing towards the detector head. The diameter of the entrance pupil is measured by first focusing on the left, then on the right edge of the pupil. The travelling distance of the image field stage represents the diameter of the entrance pupil. By choosing the proper head lens of the detector head even pupils positioned far inside of the system under test can be measured.

By convention, the modulation transfer function is normalized to unity at zero spatial frequency. For low spatial frequencies, the modulation transfer function is close to 1 (or 100%) and generally falls as the spatial frequency increases until it reaches zero. The contrast values are lower for higher spatial frequencies as shown above. As spatial frequency increases, the MTF curve falls until it reaches zero. This is limit of resolution for a given optical system or the so called cut off frequency (see figure below). When the contrast value reaches zero, the image becomes a uniform shade of grey.

Robert T. Sutter, Thomas J. Fellers and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.

ImageMaster® HR 2ImageMaster® HR MAX ImageMaster® HR MAXImageMaster® Universal ImageMaster® HR TempControlMeasurement service (ImageMaster® HR TempControl)

The depth of focus can be determined using a “through focus scan” of the MTF and setting appropriate tolerances for the drop in MTF. The depth of focus between the set tolerances will be measured and displayed.

Due to the fact that the light oscillates back and forth in a laser cavity, the phenomenon of resonance becomes a factor in the amplification of laser intensity. Depending upon the wavelength of stimulated emission and cavity length, the waves reflected from the end mirrors will either interfere constructively and be strongly amplified, or interfere destructively and cancel laser activity. Because the waves within the cavity are all coherent and in phase, they will remain in phase when reflected from a cavity mirror. The waves will also be in phase upon reaching the opposite mirror, provided the cavity length equals an integral number of wavelengths. Thus, after making one complete oscillation in the cavity, light waves have traveled a path length equal to twice the cavity length. If that distance is an integral multiple of the wavelength, the waves will all add in amplitude by constructive interference. When the cavity is not an exact multiple of the lasing wavelength, destructive interference will occur, destroying laser action. The following equation defines the resonance condition that must be met for strong amplification to occur in the laser cavity :

To completely characterize the imaging performance of an optical system, the MTF must be measured at different positions within the field of view. The MTF measurement within the field of view is known as off-axis measurement. In order to achieve an off-axis measurement, the target is moved in the field of view at the desired object position and the image analyzer to the corresponding image position.

Many years of experience with a wide range of customer requirements have been incorporated into the development of the ImageMaster® HR 2. The improvements achieved result in an extended usability for customers, high repeatability, ease of operation, modern design and a clean look-and-feel.

In addition to determination of the MTF, the key measurement parameter is the change in both the flange focal length and effective focal length when the temperature changes.

We provide Collimating Lenses to extract the collimate beam from the optical fiber or let it into the optical fiber. Anti-reflection coating is available.

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Sample Holders for various diameters and a lifting table for large samples are available for the Image Master® Universal.

The MTF measurement can be accomplished at a single wavelength or in a spectral range covering a finite band of wavelengths. The resulting measurement data are known as monochromatic or polychromatic MTF values, respectively.

Proximity sensors in vehicles are an important feature for driver assistance systems. They operate in the short infrared spectrum (SWIR), so a suitable measurement system is required to test the image quality. Moreover, measurement in SWIR spectrum becomes more important, for smartphone lenses. With a measurement accuracy of ±0.03 MTF and reproducibility of ±0.01 MTF the system meets the highest requirements even for small apertures.

For medium and larger lenses, e.g. in camera lens manufacturing and the development of aerial lenses or lenses for space exploration, the horizontally mounted ImageMaster® Universal offers the highest accuracy and maximum stability.

Our customers in R&D benefit from highly precise and repeatable measurement results. The wide range of measurement parameters leads to high efficiency in research and development as well as in prototype testing and production.

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The versatile functionality and high performance make the user-friendly ImageMaster® MTF Studio software package the preferred choice for R&D and laboratory work. High-performance functions help the user to optimize the measurement processes.

Manufacturing errors, assembly and alignment errors in the optics will deteriorate the overall imaging performance of the system. As a result, in the image, bright highlights will not appear as bright as they do in the object, and dark or shadowed areas will not be as black as those observed in the original patterns. In general an illuminated target can be defined by its spatial frequency (number of bright and dark areas per millimeter) and the contrast (the apparent difference in brightness between bright and dark areas of the image).

In addition to military and aerospace applications, cameras are also being used in the automotive industry as safety-critical systems whose properties must be tested and ensured across a broad temperature span.

The modulation transfer function varies not only related to the spatial frequency but also with the position in the field of view. The MTF measurement along the axis of symmetry of the optical system is known as on-axis measurement.

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Measuring the imaging properties of optical systems, the user of the ImageMaster® HR 2 is supported by the equally newly developed software MTF Studio.

This procedure requires a comparatively large number of measurement points with accurately known object angles and field positions. For this reason ImageMaster® instruments with dedicated distortion measurement option feature a high precision angular encoder for the object generator (accuracy 5 arcsec) and a high precision linear encoder for the image field stage (accuracy 0.2 μm). This way, the EFL is calculated as an absolute quantity, not depending on calibration parameters.

MTF

The ImageMaster® HR 2 and Universal are available in numerous variants and also enable with different collimator options, e.g. mirror collimators, precise measurement of samples with large focal length ranges. For optical systems that are used under different temperature and weather conditions, measurements in a wide temperature range are possible with the ImageMaster® HR TempControl.

LensMTF

The automated ultra-precision afocal unit is available as upgrade for afocal samples. With different autocollimator lenses for the afocal unit measurement in different wavelength ranges can be executed.

In this so-called finite-finite imaging condition the illuminated slit or crosshair target is directly moved in the object plane of the sample. In the more common infinite-finite imaging condition, the illuminated slit or crosshair is part of a collimator projecting the target to infinity. The collimator is then oriented at different off axis angles for characterizing the MTF at the corresponding image fields. Figure 4 shows the typical setup for this imaging condition.

The grids shown are actually no longer used in order to measure the MTF. Modern MTF-Testers like the ImageMaster® use a single illuminated slit on opaque background as the object. From a mathematical point of view a single slit can be regarded as the sum over all spatial frequencies (Fourier synthesis). All frequencies contribute with the same amplitude (=1) to this slit not taking the finite slit width into account for this description. This single slit will be imaged into the image plane of the sample. Due to diffraction and aberrations there will be no perfect slit image in this plane, instead the slit image is broadened. It represents the so called Line Spread Function (LSF). On the basis of Fourier analysis the contribution of each spatial frequency to the LSF can be calculated. Actually the amplitude of each spatial frequency is equal to the contrast at this frequency. The Fourier analysis of the Lines Spread Function corresponds to the MTF of the sample. Taking a single image of the LSF unveils the complete MTF. Alternatively it is also possible to use a cross (i.e. two perpendicular slits) for the target. This enables the ImageMaster® to measure the MTF in two image directions simultaneously provided a CCD camera is used for the image analyzer. And finally a pinhole target can be used as the object, too. The image of a pinhole target is called Point Spread Function. This function contains the complete MTF information in all image directions. The basic terms and mathematical relations used for MTF are described in the ISO 9334 standard.

The ImageMaster® HR 2 is our completely redesigned new version of the long-time successful ImageMaster® HR – the worldwide standard for image quality testing of small and medium-sized lenses e. g. for smartphone-, photo- and film cameras.

If the angle is positive, the image rotates clockwise. If the angle is negative, the image rotates counterclockwise. ... The image is flipped and enlarged. Then, ...

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.

The wide model range of ImageMaster® HR 2 and Universal allows measurement of a large number of optical parameters over a wide spectral range. The ImageMaster® HR can be used to measure lenses in the spectral range NUV-VIS-NIR-SWIR-MWIR-LWIR. The ImageMaster® Universal is flexibly suitable for MTF Testing in the entire spectral range UV-VIS-NIR-SWIR-MWIR-LWIR from 200 to 13,000nm.

Contrast vs spatial frequency. This figure shows the MTF of the diffraction limited optics and a measured MTF referring to Fig. 1

A common misconception about lasers results from the idea that all of the emitted light is reflected back and forth within the cavity until a critical intensity is reached, whereupon some "escapes" through the output mirror as a beam. In reality, the output mirror always transmits a constant fraction of the light as the beam, reflecting the rest back into the cavity. This function is important in allowing the laser to reach an equilibrium state, with the power levels both inside and outside the laser becoming constant.