® COPYRIGHT 2015 EDMUND OPTICS, INC. ALL RIGHTS RESERVED 02/15 Europe | Asia | 962 687 481 343 240 175 120 +49 (0) 721 6273730 +33 (0) 8 20 20 75 55 1374 1000 µm/mm GERMANY: FRANCE: 0% Contrast Limit (lp/mm) @ 0.520 µm Edmund Optics USA Optics Edmund Diffraction Limit = f/# x wavelength (in µm) 2 4 8 11 16 2.8 5.6 1.4 f/# Do you have questions? Contact us today! Contact questions? have you Do The diffraction limit calculated at different f/#s for 520 nm light (green light) www.edmundoptics.eu/eo-imaging request your Imaging Optics Catalog. your to request UK: +44 (0) 1904 788600 [email protected] Visit Table 1: Table Equation 1

Diffraction Limit

Modulation Transfer Function (MTF) curves are used to Function Transfer Modulation ing Lens Design Limitations Lens Design ding erstan Und After the diffraction limit is reached, the lens becomes incapable of of becomes incapable the lens reached, is limit the diffraction After 1 limit detailed in Table diffraction The resolving greater frequencies. numbers may These frequencies. given contrast at 0% for shows appear rather high, but are strictly theoretical – a number of other First, as a general rule, must also be considered. practical factors at or near 0% contrast. imaging sensors cannot reproduce information to 10% Due to inherent noise, contrast generally needs to be above imaging avoid To be reliably detected on standard imaging sensors. complications, it is recommended to target 20% contrast or higher at lens aberrations Additionally, critical lp/mm resolution. the application’s reduce tolerances also associated with manufacturing and variations performance. a sensors capabilities utilize determine whether a lens will effectively requirements. and fulfill the desired application’s Every lens has an absolute upper performance limit dictated the Every lens has an absolute upper performance by f/# of the the working limitationby This is controlled of physics. laws of light that pass through the lens. Known lens and the wavelength(s) Limit, this limitation in line pairs/mm and is given as the Diffraction of the lens. Even power determines the theoretical maximum resolving This limited. design will be diffraction lens that is not limited by a perfect are no longer distinguishable Airylimit is the point where two patterns that limit, a simple formula calculate the diffraction To other. from each of light can be used relates it to the f/# of the lens and the wavelength more about f/# in our Imaging Optics Catalog. (Equation 1). Learn eo-imaging www.edmundoptics.eu/ ® COPYRIGHT 2015 EDMUND OPTICS, INC. ALL RIGHTS RESERVED 02/15

150.0 Europe | Asia | 150.0 150.0 +49 (0) 721 6273730 +33 (0) 8 20 20 75 55 (Continued on next page) 5µm 5µm 5µm 75.0 75.0 75.0 GERMANY: FRANCE: Edmund Optics USA Optics Edmund Spatial Frequency in Cycles Per mm Spatial Frequency in Cycles Per mm 10µm 10µm MTF: f/2.8, 150mm WD, 12mm fl MTF: f/2.8, 200mm WD, 12mm fl Spatial Frequency in Cycles Per mm 10µm Pixel Size: MTF: f/2.8, 150mm WD, 12mm fl MTF: f/2.8, 150mm Pixel Size: 0.0 0.0 0 0

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100 Contrast (%) Contrast Do you have questions? Contact us today! Contact questions? have you Do and system parameters MTF curves for two lens designs (a and b) with the same focal length, f/#, MTF curve for a 12 mm lens used on the Sony IXC 625 sensor UK: +44 (0) 1904 788600 [email protected] Figure 2a Figure 2b Figure 1

Figure 2: Figure 1: associated with detail reproduction that is not in the center of the FOV. lens will produce spots that are not com- a effects, Due to aberrational and in the horizontal sizes different have pletely round and will therefore spots blending together leads to variation size This orientation. vertical and produces different in one direction than the other, more quickly It is very im- at the same frequency. axes in different contrast levels when of these two values port to consider the implications of the lower to advantageous generally is It application. a given for lens a evaluating highest gain the to sensor entire the across level contrast the maximize in a system. of performance levels - - - Figure 2a is , tremendous 2a, Figure will excel in both lower resolution and demanding resolution in both lower Figure 2a will excel rves d MTF Cu (MTF) an Function ransfer ation T Modul xample 1: Comparison of two different lens designs lens designs Example 1: Comparison of two different at f/2.8 with the same focal length (fl), 12 mm, coming both design constraints and fabrication variations; variations; and fabrication design constraints coming both design and tighter manufacturing more complex associated with a much tolerances. distances larg- short working for resolution applications where relatively best where more pixels are required. Figure 2b will work of view er field are needed to enhance the fidelity of image processing algorithms and where they situations lenses have cost is required. Both where lower depending on the application. choice, are the correct examines two different lenses of the same focal length that lenses of the same focal two different Figure 2 examines lenses will produce systems These and f/#. sensor, the same FOV, have the hori- In analysis, in performance. but differ that are the same size demonstrates that zontal light blue line at 30% contrast on Figure 2a essentially everywhere within the at least 30% contrast is achievable the entire capability for of the sensor to be well- will allow which FOV, This 30% contrast. is below Figure 2b, nearly half the field For utilized. at half of the image quality will only be achievable means that better curvesboth on the represents box orange the note, to Also sensor. lens in Figure 2b with performance intercept frequency of the lower on placed is box same that When contrast. 70% between these lenses is the cost associated with over difference The u frequencies between at lower can be seen even difference performance the two lenses. Configurations and Designs Lens Comparing Additionally, it can be seen that there are two green and two red lines. it can be seen that there are two green and two red lines. Additionally, contrast components lines represent the tangential These and sagittal is an example of an MTF curve for a 12 mm lens used on the an MTF curve a 12 of for Figure 1 is an example of ⅔” and 3.45 µm pix has a sensor format which sensor, 625 IXC Sony first thing to note is The curve a variety of information. This provides line black The line. the black limit is represented by that the diffraction can be contrast that possible theoretically that the maximum indicates and that no lens lp/mm frequency, is almost 70% at the 150 achieved Additionally, higher than this. good, can perform how design, no matter - corre lines These red. and green, blue, lines: colored three are there across the sensor in the center (blue), this lens performs spond to how on the sensor (green), and the the 0.7X position at 70% of the full field that at lower It is clearly shown corner of the sensor (red), respectively. is not the same across the and higher frequencies contrast reproduction the FOV. entire sensor and, thus, not the same over MTF curves show resolution and contrast information simultaneouslyMTF curves allow information resolution and contrast show a specific applica- based on the requirements for ing a lens to be evaluated Used of multiple lenses. compare the performance tion and can be used to feasible. MTF curves if an application is actually can help determine correctly, a frequency range from 0 lp/mm curve lens contrast over The shows els. Additionally, lp/mm). 145 resolution is limiting (sensor’s lp/mm to 150 yields of 0.05X, which at 2.8 and is set at a PMAG this lens has its f/# set dimensions of 20X the horizontal mm for 170 of approximately a FOV in this section. all examples will be used for FOV/PMAG This the sensor. the simulated light source. White light is used for

eo-imaging www.edmundoptics.eu/ ® COPYRIGHT 2015 EDMUND OPTICS, INC. ALL RIGHTS RESERVED 02/15 Europe | Asia | Figure 4: MTF curves for a 35 mm lens at the same WD and different f/#s: f/4 (a) and f/2 (b) Figure 3: different high resolution Two lens designs with different focal lengths at the same f/# and system parameters Figure 5: MTF curves for a 35 mm focal length lens at f/2 with different working distances +49 (0) 721 6273730 +33 (0) 8 20 20 75 55 150 150.0 150.0 150 150.0 150.0 GERMANY: FRANCE: 5µm 5µm 5µm 5µm Edmund Optics USA Optics Edmund 75 75.0 75.0 75.0 75 75.0 Spatial Frequency in Cycles Per mm Spatial Frequency in Cycles Per mm Spatial Frequency in Cycles Per mm Spatial Frequency in Cycles Per mm Spatial Frequency in cycles per mm 10µm 10µm 10µm 10µm Spatial Frequency in cycles per mm MTF: f/2, 200nm WD, 35mm fl MTF: f/2, 200WD, 35mm fl MTF: f/2, 450nm WD, 35mm fl MTF: f/2.8, 150mm WD, 12mm fl MTF: f/2.8, 150mm WD, MTF: f/2.8, 200mm WD, 16mm fl MTF: f/4, 200mm WD, 35mm fl Pixel Size: Pixel Size: Pixel Size: Pixel Size: 0.0 0 0.0 0 0

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100 Contrast (%) Contrast Contrast (%) Contrast Contrast (%) Contrast Contrast (%) Contrast Do you have questions? Contact us today! Contact questions? have you Do UK: +44 (0) 1904 788600 [email protected] Figure 4b Figure 5a Figure 3a Figure 3b Figure 4a Figure 5b - imaging lenses which ® wo different high resolution lens designs high resolution wo different feature these MTF curves. feature www.edmundoptics.eu/imaging for for all TECHSPEC , working distancesFigure 5, working of 200 mm (a) and 450 mm (b) are Changing Working of Example 4: The Effect Distance on MTF the same 35 mm lens design f/#s of Example 3: Comparison of MTF for different xample 2: T Example 2: 16 mm at f/2.8 lengths: 12 mm and focal with different download comprehensive datasheets comprehensive to download Visit - con - 12% is only about 10 difference While the absolute Figure 3a. For For A large performance the same 35 mm lens design at f/2. for examined is directly related to the ability to balance can be seen, which difference distances. a range of working content in lens design over aberrational with refocusing, will lead to variations distance, even Changing working from its designed away moves as the lens or reductions in performance f/#s. More details on at lower are most profound effects These range. can be found in our Imaging Optics Catalog. these effects u features the MTF for a 35 mm lens design using white light a 35 mm lens design using white for the MTF Figure 4 features - con the diffraction-limited line shows yellow The at f/4 (a) and f/2 (b). Figure 4a on both graphs while the blue trast at the Nyquist limit for limit of the at the Nyquist performance actual line denotes the lowest of Figure 4b is While the theoretical limit same lens at f/4 in Figure 4a. of how is an example This lower. is much the performance higher, far greatly increasing per effects, a higher f/# can reduce the aberrational u formance of a lens, even though the theoretical performance limit is though the theoretical performance of a lens, even formance light less is resoultion besides primary The tradeoff reduced. greatly throughput at the higher f/#. examines two different high resolution lenses with focal focal lenses with high resolution two different Figure 3 examines and f/#. sensor, the same FOV, that have mm 16 mm and lengths of 12 limit of Figure 3b (light contrast at the Nyquist By looking at the lens’s compared increase can be seen when blue line), a distinct performance to is closer to 33% considering the change difference trast, the relative has Another orange box 30% contrast to 42%. from approximately this time where Figure 3a hits 70% contrast. been placed on this graph, - the previ as in is not as extreme level at this Note that the difference lenses is that the working between these tradeoff The ous example. 33% but with Figure 3b has an increase of about distance the lens in for guidelines This follows the general a decent increase in performance. Optics Catalog. outlined in our Imaging u

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f/16 15.81 18.35 20.30 25.77 34.36 Image Plane Europe | Asia | f/8 7.91 9.17 10.15 12.88 17.18 f/4 3.95 4.59 5.08 6.44 8.59 +49 (0) 721 6273730 +33 (0) 8 20 20 75 55 Aperture (f/#) (Continued on next page) 2.77 3.21 3.55 4.51 6.01 f/2.8 GERMANY: FRANCE: 1.38 1.61 1.78 2.25 3.01 f/1.4 Edmund Optics USA Optics Edmund 405 470 520 660 880 (nm) , relates to the ability of a lens to focus all the abilityFigure 7, relates to focus to lens of a Wavelength Minimum spot size (Airyµm = 2.44 x λ (µm) x f/# Disk diameter) in Do you have questions? Contact us today! Contact questions? have you Do Red Blue Chromatic Focal Shift Color Theoretical Airy Disk diameter spot size (in µm) for various wavelengths and f/#s Green Violet UK: +44 (0) 1904 788600 [email protected] NIR (Near-Infrared) Figure 7 Equation 2 Figure 7: Choosing the Optimal Wavelength eliminating both illumination enhances contrast by Monochromatic - It is readily avail aberration. and lateral chromatic shift focal chromatic of LED illumination, lasers, and through the use of able in the form MTF effects different can have wavelengths different filters. However, limit defines the smallest theoretical spot diffraction The in a system. Airyby the Disk lens, as defined a perfect be created by can which our Imaging (λ) dependence. See has a wavelength which diameter, limit. Airy Disk and diffraction Optics Catalog for more details on the both for in spot size the change Using the Equation 2, one can analyze f/#s. and different wavelengths different Table 2: Table , shift focal Chromatic - wave from the lens. Different at the same distance away wavelengths with in focus shift This planes of best focus. different lengths will have since the different results in reduced contrast, respect to wavelength plane where the spots at the image size create different wavelengths of Figure 7 a small spot located. In the image plane camera sensor is in green, and the largest a larger spot size in the red wavelengths, size all at once. Not all colors will be in focus is shown. in blue spot size be found in our Imaging Optics Catalog. Advanced details can - Advanced details may be found ffects on Performance ffects length E Wave , can be seen as you move from the center move Figure 6, can be seen as you Lateral Color Shift Figure 6 Figure 6: features the calculated Airy disk diameter for wavelengths rang- Airy wavelengths the calculated for disk diameter 2 features Table This f/#s. various nm) at (880 Near-Infrared to (405 nm) Violet from ing resolution theoretical better have systems lens that datashows clearly The wavelengths. shorter with utilized are they when performance and wavelengths to understanding First, shorter this are multi-fold. benefits due regardless of size pixels utilization of the sensor’s better for allow is especially pronounced on This spot size. to the smaller achievable to more flexibility for Second, it allows sensors with very small pixels. example, For greater depth of field. for will allow use higher f/#s, which of 4.51 µm or a red LED could be used at f/2.8 to generate a spot size at f/4. a blue LED could be used to generate almost the same spot size at best focus, of performance If both options yield acceptable levels depth of field, produce better set at f/4 using blue light will the system requirement. critical a be could which in our Imaging Optics Catalog. ner of the image, wavelengths tend to separate and produce a rainbow tend to separate and produce a rainbow ner of the image, wavelengths point on the object a given a result of this color separation, As effect. in reduced contrast. On sensors a larger area, resulting is imaged over more pronounced, as the blurring this result is even with smaller pixels, In depth details on lateral color can be found more pixels. spreads over in our Imaging Optics Catalog. , color shift Lateral for the spots the image. In the center, the edge of of the image towards cor the towards Moving concentric. are light of wavelengths different Chromatic Aberrations Chromatic lateral color shift in two fundamental exist forms: Chromatic aberrations (Figure 7). shift focal (Figure 6) and chromatic Different wavelengths bend at different angles as light passes through as light passes angles different bend at wavelengths Different is commonly observed when This etc.). air, a medium (glass, water, shorter effect; a prism and creates a rainbow sunlight passes through creates same effect This are bent more than longer ones. wavelengths problems when trying details in imag- and gain information to resolve systems vision machine and imaging this issue, avoid To systems. ing single only involves which illumination, monochromatic use commonly illumi- Monochromatic bands of the spectrum. or narrow wavelengths eliminates what are known practically nation, e.g.LED, from a 660 nm in an imaging system. aberrations as chromatic eo-imaging www.edmundoptics.eu/ ® COPYRIGHT 2015 EDMUND OPTICS, INC. ALL RIGHTS RESERVED 02/15 (a) and Europe | Asia | 150 150 150 150 Each image is from the center of Each image is from of a multi ele- the field of view elements of ment star target. The visu- for the allow target a star resolution alization of changing produced by a lens and camera Higher in all directions. system resolutions are observed closer to the center of the star where the producing lines become narrower, higher frequencies. +49 (0) 721 6273730 +33 (0) 8 20 20 75 55 75 75 75 75 GERMANY: FRANCE: Edmund Optics USA Optics Edmund Spatial Frequency in cycles per mm Spatial Frequency in Cycles Per mm Spatial Frequency in Cycles Per mm Spatial Frequency in Cycles Per mm White Light Diffraction MTF 470nm Illumination Diffraction MTF 470nm Illumination Diffraction MTF 405nm Illumination Diffraction MTF Figure 8b 0 0 0 0 0 0 0 0

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Contrast (%) Contrast Contrast (%) Contrast Contrast (%) Contrast Contrast (%) Contrast MTF curves for a 35 mm lens at f/2 with 470 nm (a) and 405 nm (b) wavelength MTF curves for the same lens at f/2 using a different wavelengths; white light 470 nm (b) Images of a star target taken with the same lens, at the same f/#, with the same sensor. the same lens, at the same f/#, with the same sensor. Images of a star target taken with nm (a) to 470 nm (b) The wavelength is varied from 660 UK: +44 (0) 1904 788600 [email protected] Figure 8a Figure 10a Figure 10b Figure 9a Figure 9b Figure 10: illumination Figure 9: Figure 8: - - has Figure 10a (10a and 10b respectively)While . 10b and (10a More details on the phenomenon in our Imaging phenomenon the on details More (detailed in our Imaging Optics Catalog). heoretical Limitations Example 3: Theoretical onochromatic MTF vs. Monochromatic Example 2: White Light mprovement with Wavelength with Improvement Example 1: - Figure 9b is using 470 nm illumi Figure 9a is using white light, and , the same lens is used at the same working distance and at the same working Figure 9, the same lens is used has a significant increase in resolvable in resolvable has a significant increase Figure 8a. Note that Figure 8b a lower diffraction limit, it also shows that the 470 nm wavelength yields wavelength 470 nm the that shows also it limit, diffraction lower a here is increased The effect positions. at all field higher performance f/# of its design capabilities for when the lens is used at the extremes and WD is performance issue that can greatly affect Another wavelength range wavelength the application’s As shift. focal related to chromatic will of performance ability to maintain high levels increases, the lens’s compromised. be Optics Catalog. compares a 35 mm lens at f/2 with blue (470 nm) and violet Figure 10 nm) wavelengths (405 u is at the violet wavelength of 405 nm, but most 2 is at the violet wavelength mance seen in Table very important to in this area. It’s well designs cannot perform system using wavelengths short such at do realistically can lens a what evaluate curves. lens performance A few issues can arise with changing wavelength that need to be un- wavelength issues can arise with changing A few the further into the blue a lens design perspective, derstood. From the more a become shorter, wavelengths as portion of the spectrum, that the waveband narrow of how regardless lens design can struggle at shorter well tend to not perform glass materials is used. Essentially, but they in this region of the spectrum, Designs do exist wavelengths. materials that may limited in their capabilities, and the exotic are often best theoretical perfor The be required to build the lens can be costly. Wavelength Considerations Wavelength u In f/#. at the is at 50% or below nation. In Figure 3.9a, all of the performance limit Nyquist at the of the performance all 9b , Figure For limit. Nyquist in the center of the performance Additionally, is higher than Figure 9a. limit of Figure 9a. The the diffraction in Figure 9b is above rea - system using monochromatic is twofold: this increase in performance son for generally al- which in the system aberrations light eliminates chromatic is illumination and 470 nm created, to be smaller spots much for lows range visible in used is that light of wavelengths shortest the of one Airy limit and Disk, detailedAs imaging. in the sections on diffraction of resolution. higher levels for allow shorter wavelengths rational effects. This allows diffraction to be the primary limitation diffraction in the allows This rational effects. at of the limiting resolution representative blue circles are The system. in frequencies finer detail). at the lower detail 50% Even (approximately nm illumination of contrast with 470 higher level (wider lines), there is a in Figure 8b. u and camera with the same lenses in Figure 8 are taken images Both same spatial reso- thus presenting the of view, same field producing the The 3.45 µm pixels. camera utilizes The object in lp/mm. lution on the is set at 660 nm and Figure 8b at 470 nm. illumination used in Figure 8a aber reduce any set to higher f/# to greatly lens was high resolution The eo-imaging www.edmundoptics.eu/