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Hi, I am currently working on calculating MTF. I had some confusions I wanted to clarify. 1. I have the LSF with the x-axis represented by samples. I took a sampling rate of 0.01 mm and so my LSF is made up of 2000 samples making it equal to 20 mm. After taking the Fourier transform I get the MTF. Now I want the x axis to display lp/mm rather than number of samples. Does 2 samples make 1 line pair? So then I have 1000 samples in total spread over 20 mm? Making 50 cycles/mm. So while representing my MTF the x axis should consist of equally spaced 1000 points?

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A standard zoom lens covers wide-angle to telephoto focal lengths around 50mm. In addition to snap shots and portraits, these lenses prove their worth in a wide variety of shooting scenarios such as landscapes at the wide end and shots of animals and buildings at the telephoto end.

As explained above, focal length is a very important figure, but when choosing a lens you also need to be mindful of the sensor size on your camera body. With digital SLR cameras, light reaching the image sensor is stored as an electrical charge, and an image is created based on the color information obtained through the color filter. These image sensors come in mainly two types: 35mm full-frame, and APS-C. The size of a 35mm full-frame sensor is 36mm x 24mm. The larger the sensor size allows a wider area to be captured with greater sensitivity and its rich gradation. On the other hand, the size of an APS-C sensor is a step smaller at 23.5mm x 15.6mm* and captures narrower area. *APS-C image sensor sizes vary by camera. Therefore, you will need a lens that is compatible with the sensor size of the camera body. Camera lenses have a specific sensor size that they are compatible with, so choose a lens that is compatible with the camera you have. When APS-C camera is used, you will need to do some calculation to figure out the real coverage. The angle of view of each focal length depends on the sensor size. Generally, focal lengths and angles of view are based on 35mm full-frame size, so when selecting an APS-C compatible lens, it is easier to understand the angle of view when converted to full-frame size. Such conversion is known as '35mm equivalent'. In general, the focal length of APS-C lenses can be converted to the focal length of lenses for full-frame cameras by multiplying the focal length by 1.5 (for Sony, Nikon and 1.6 for Canon). The relationship between angle of view and focal length can be mapped as shown in the table below, which you can use as a reference when selecting a lens for APS-C.

Two lines is one line pair or – interchangeably if you are a person of science – a cycle. The cycle refers to the bright to dark to bright transitions, in the case of the line pair above it goes peak-to-peak in 2.5 pixels. Spatially we would say that the period of one cycle (or one line pair) is 2.5 pixels. Frequency is one over the period so we could also say that the spatial frequency corresponding to this line spacing is 0.4 cycles/pixel ( or equivalently line pairs per pixel pitch).

Recall that the MTF curve above is a one dimensional result which only applies in the position on the sensing plane corresponding to the center of the edge, in the direction normal to the edge.

As ultra-telephoto zoom lenses allow you to enlarge the faraway subjects, they are best suited for shooting subjects you cannot get close to, such as wildlife, sporting events held at large venues, aircraft and trains. By combining the compression effects and bokeh that telephoto zooms are known for, you can also compose more appealing images.

Line pairs per mmand pixel size

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The MTF is normalized to one at the origin by definition. One means all possible contrast information present in the scene was transferred, zero means no spatial resolution information (detail) was transferred to the raw file. The MTF curve below shows how much the contrast of a figurative set of increasingly closer ‘lines’ above is attenuated as a function of the spatial frequency (one divided by the given spatial separation) indicated on the horizontal axis. As we have seen the units of spatial frequency on the sensor are naturally cycles per pixel pitch, or just cycles/pixel for short.

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Another characteristic of focal length is depth of field. Depth of field refers to the range in which the image looks it is in focus, and a deep depth of field means that the image looks in focus through wide range, such as from a subject to background. And if the depth of field is shallow, only the area around the subject will be in focus and the background will have a smooth bokeh. The shorter the focal length of the lens and the larger the aperture (F-number), the deeper the depth of field. This is why wide-angle lenses are suitable for landscape photography, as the short focal length increases the depth of field and allows the photographer to capture details in the background clearly. On the other hand, as telephoto lenses have a long focal length and shallow depth of field, the bokeh in the background of a subject is more pronounced. By utilizing these bokeh effects, you can capture portraits and other images where the subject stands out against the background.

The slanted edge method relies on information from the raw data only. It doesn’t know how tall the sensor is or how far apart the pixels are physically. Without additional information it can only produce the MTF curve as a function of the units for distance it knows: samples at pixel spacing in the raw data. So cycles per pixel pitch (often shortened to cycles/pixel, cy/px or c/p) are the natural units of the MTF curve produced by the slanted edge method.

By convention the displayed image is assumed to be viewed in landscape orientation, so spatial resolution per picture ‘height’ is normally calculated by multiplying by the shorter sensor dimension. One could make a case that the length of the diagonal should be used instead to somehow level the playing field when aspect ratios differ significantly between sensors – but aspect ratio typically only makes a small difference to the final result so in practice it is often ignored.

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Sometimes line widths (lw) are used instead of line pairs (lp) or cycles (cy). It’s easy to convert between the three because there are two line widths* in one line pair ( or equivalently one cycle), so 1351 lp/ph correspond to 2702 lw/ph.

Good question though beyond the scope of this page, you can find the answer at the bottom of this article. If you can’t figure it out send me an email via the form and I will help you.

Watch how the units cancel out to yield cycles per mm. One cycle is equivalent to one peak-to-peak contrast swing – or a line pair (lp). Units of line pairs per mm (lp/mm) are useful when interested in how well an imaging system performs around a specific spot of the capture (say the center), in the direction normal to the edge.

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The same result could have been obtained simply by multiplying the original measurement in cycles per pixel pitch by the number of pixels on the side of the sensor. For instance the D800e has 4924 usable pixels on the short side, so in lp/ph that would be

The 17-70mm F/2.8 Di III-A VC RXD (Model B070) is a large-aperture standard zoom lens for APS-C format mirrorless cameras. With a focal length range of 17mm to 70mm (a full-frame equivalent of 25.5-105mm) for daily use, this achieves a 4.1x zoom. The optical design ensures high resolution and high contrast not just in the center of the image but also in corners and at the edges. The quiet AF drive motor and the VC image stabilization mechanism facilitate hand-held shooting. In addition, by counteracting focus breathing, the 17-70mm F2.8 empowers users' expression of their creative intentions to the fullest degree. This highly practical lens allows you to easily enjoy the high image quality of a large F2.8 aperture for both still and video shooting.

Hi Ted, your memory serves you well, though those patterns are repeating. An ideal step function on the other hand is a single discontinuity so it gives rise to all frequencies at once, albeit of energy varying with 1/f (so with a discontinuity at the origin). The derivative of an ideal step function is a single impulse, which of course has equal energy throughout the spectrum (not so if it repeated regularly). And that’s what we compare the performance of an imaging system to with measured MTF.

The 50-400mm F/4.5-6.3 Di III VC VXD (Model A067) is an ultra-telephoto zoom lens with an 8x zoom starting at 50mm at the wide-angle end and compatible with full-frame mirrorless cameras. The lens delivers uncompromised high image quality over the entire 50-400mm focal length range, yet is as compact and lightweight as a 100-400mm class lens. Equipped with the VXD mechanism and the VC mechanism, the lens can quickly focus on the subject's movement when shooting sports and wild birds. The 50-400mm F4.5-6.3 VC is a new ultra-telephoto zoom lens that combines unparalleled image quality and mobility.

One may be interested to know at what spatial frequency the imaging system is only able to transfer half of the possible captured contrast to the raw data. We can simply read off the curve the frequency that corresponds to an MTF value of 1/2, customarily referred to as MTF50(%). In this case we can see above that MTF50 occurs when the imaging system is presented with figurative lines of detail alternating at a spatial frequency of about 0.27 c/p (that is the peaks of a line pair are separated by one over that, or about 3.7 pixels). If one does not have access to the whole curve, MTF50 is considered to be a decent indicator of perceived sharpness when pixel peeping.

The 150-500mm F/5-6.7 Di III VC VXD (Model A057) is compact enough to be handheld while maintaining a focal length of 500mm on the telephoto end. It allows users to easily enjoy the world of the 500mm ultra-telephoto lens while maintaining its high image quality. The high-speed, high-precision AF with excellent tracking performance and the VC mechanism support handheld shooting in the ultra-telephoto range.

Line pairs per mmradiology

This post will address the units involved in spatial resolution measurement using as an example readings from the popular slanted edge method, although their applicability is generic.

The 70-300mm F/4.5-6.3 Di III RXD (Model A047) for full-frame mirrorless cameras is a telephoto zoom lens designed and created so photographers of all skill levels can enjoy high quality images comfortably. The 70-300mm F4.5-6.3 covers a broad telephoto zoom range yet is the small and lightest weight. With special emphasis on resolving power, TAMRON has deployed special lens elements appropriately arranged to correct chromatic aberration, generally very strong in a telephoto lens, as well as other aberrations. Users can enjoy high-resolution images combined with stunning bokeh qualities that are achievable only with a telephoto lens. The lens also incorporates the RXD, a high-speed precision AF drive system that is remarkably quiet. The 70-300mm F4.5-6.3 is a versatile lens for photographing landscapes, sports and other action, pets, wildlife, and more. The lens also demonstrates its potential for portrait shooting, casual snapshots, and scenarios that require you to be mobile and shoot handheld, like sporting events.

Great article. Long time EO engineer and love to have these types of break downs to convey topics. I teach/mentor junior engineers and examples like your blog are fantastic. I won’t copy anything but will suggest this and other articles as references for others to go see. I’m also a amateur photographer and again, sites like these are great. I don’t appreciate the “beginner” sites where they start off with $10k worth of equipment and tell you everything you know is wrong. Your insights are very helpful and the photos are beautiful. Thank you for taking the time to so this. I’m glad I found your site!

70-180mm F/2.8 Di III VC VXD G2 (Model A065) has evolved to G2 level.This is the world’s smallest and lightest, fast-aperture telephoto zoom lens for Sony E-mount with astounding portability and superb image quality.

The 17-28mm F/2.8 Di III RXD (Model A046) achieves a filter diameter of ø67mm, which is surprising for a large aperture ultra wide-angle zoom lens for full-frame cameras. It’s small and light weight with a good camera balance. It's a dedicated lens for mirrorless interchangeable -lens cameras that can be carried easily and can be used in various situations.

The slanted edge method starts by generating an Edge Spread Function (ESF) from a matrix of sampled pixel data stored in the raw file of the captured edge image.

The 50-400mm F/4.5-6.3 Di III VC VXD (Model A067) is an ultra-telephoto zoom lens with an 8x zoom starting at 50mm at the wide-angle end and compatible with full-frame mirrorless cameras. The lens delivers uncompromised high image quality over the entire 50-400mm focal length range, yet is as compact and lightweight as a 100-400mm class lens. Equipped with the VXD mechanism and the VC mechanism, the lens can quickly focus on the subject's movement when shooting sports and wild birds. The 50-400mm F4.5-6.3 is a new ultra-telephoto zoom lens that combines unparalleled image quality and mobility.

The units of the horizontal axis are still the distance between two contiguous pixels in the direction under consideration:

When light enters a lens, the point where the light gathers is called the focal point. While light travels in a straight ray, when it passes through a lens it refracts and is concentrated at a single point so called focal point. When a light passes through a lens and at this focal point it forms an image, when an image sensor is placed at this position, the image can be captured. A focal length is a distance from the center of the lens (principal point) to the image sensor, and this is an important value that characterizes a lens.

What would happen on the imaging plane if we had more than one such line, parallel and side by side? Assuming the lines were the result of incoherent light (mostly true in nature) linearity and superposition would apply so the aggregate pattern of intensity on the imaging plane would simply be the sum of the individual LSFs, point by point, as represented by the continuous red curve below. That’s the intensity profile that would be recorded in the raw data from projections of two distant perfectly thin lines against a black background.

Linepair resolution

Here are TAMRON's recommended lenses by lens type. TAMRON zoom lenses cover a wide range of focal lengths with a single lens yet are of a size that makes them easy to carry. On top of this, they are characterized by their high descriptive performance and close-up shooting ability. We hope you will find the lens that suits you best.

In normal, well setup photographic applications with in-‘focus’ quality lenses, MTF curves of unprocessed raw image data captured with good technique decrease monotonically from a peak at zero frequency (also known as DC). Zero frequency would occur if the distance between two lines (the period) were infinite – In such a case no matter how wide each individual line spread function is, the system is assumed to be able to transfer all possible contrast in the scene to the raw data, represented by the normalized value of 1. For more on the properties of the MTF see the following article on Fourier Optics.

The slanted edge method produces the Modulation Transfer Function (MTF) of a given target and hardware setup, that is a curve that shows how well detail is transferred from the scene to (ideally) the raw data. The natural units of spatial resolution information on the sensor so obtained are cycles per pixel pitch. To see why let’s follow the method step by step.

lp/mm to resolution

In this case, the total magnification of a microscope is equal to the magnification of the objective ocular lens multiplied by the high-power objective lens.

The wider the line spread function and/or the closer the two lines are spaced, the more the overlap and the more the lost contrast – hence the more the lost ‘sharpness’ and the less the detail we are able to discern in the image.

11-20mm F/2.8 Di III-A RXD (Model B060) is the world's first compact, lightweight F2.8 ultra wide-angle zoom lens for Sony E-mount APS-C mirrorless cameras. Can be a great choice for video shooting.

Product Page | 11-20mm F/2.8 Di III-A RXD (Model B060) is the world's first compact, lightweight F2.8 ultra wide-angle zoom lens for Sony E-mount APS-C mirrorless cameras. Can be a great choice for video shooting.

The 35-150mm F/2-2.8 Di III VXD (Model A058) is a high resolution travel zoom lens that covers everything from the 35mm wide angle to the 150mm telephoto focal length, the first zoom lens achieving an aperture of F2 at the wide angle end. It has a groundbreaking fast-aperture and utilizes the linear motor focus mechanism VXD (Voice-coil eXtreme-torque Drive), thereby achieving high speed, high precision autofocusing. The innovative lens design enabled us to greatly improve the lens's grip and functionality. The software, developed in-house, enables to easily customize functions and to update firmware.

lp/mm to pixel size

Telephoto zoom lenses enable photographers bring the subject closer, making them ideal for events such as sports events, as well as for birding and wildlife. They are also useful in natural landscapes photographed in conjunction with trekking, hiking and mountaineering.They are also recommended for impressive portrait photography with naturally blurred backgrounds and compression effects.

In the face of these many variables the data found on many sites is often the average of perpendicular (tangential and sagittal) MTF readings tested in several spots throughout the field of view. Read the fine print of each site to figure out where they test and how they aggregate the data.

The 20-40mm F/2.8 Di III VXD (Model A062) is a new large-aperture standard zoom lens that thoroughly pursues portability. While covering the range from the ultra-wide angle of 20mm to the standard range of 40mm, it is the smallest and lightest in its class. It also offers high image quality throughout the entire zoom range, making it useful not only for still image shooting but also for video recording such as vlogging. The VXD, which is quiet and agile, achieves high-speed, high-precision autofocusing. It is a new, unprecedented large-aperture standard zoom lens that allows users to easily enjoy taking out and shooting both still and video.

Assuming you are using an edge with MTF Mapper, it outputs the MTF curve in units of cycles/pixel. To convert it to lp/mm all you have to do is figure out how long a pixel is (its pitch). If it is 0.005mm, then you simply divide the output in cycles/pixel by 0.005.

Fortunately there is a mathematical operation that will determine the amount of energy present at each frequency once fed intensity functions like our LSF: the Fourier Transform. The original signal from the sensor in the raw data is said to be in the Spatial Domain. After Fourier transformation the result is said to be in the Frequency Domain and often presented as the Power or, in our case, Energy Spectrum of the original signal.

Jan 7, 2021 — Indicates the resolution units. Used for images with a non-square aspect ratio, but without meaningful absolute dimensions.

28-75mm F/2.8 Di III VXD G2 (Model A063) is the second-generation fast-aperture standard zoom lens for Sony and Nikon full-frame mirrorless cameras, offering significantly improved optical and autofocus performance and new function customization.

Lens aberrations of even excellent lenses vary substantially with direction and throughout the field of view – so MTF should be measured in more than one direction and in various key spots in the field of view in order to determine more completely the actual performance of the imaging system.

* The use of ‘Lines’ is inherited from the post war period (see Duffieux, Kingslake, etc.) when ‘definition’ and ‘resolving power’ were determined by capturing images of something similar to the 1951 USAF target below (wikipedia commons license):

The dark portion of the edge is on the left, the bright portion is on the right. The vertical axis represents raw levels normalized to 16 bit precision, which are proportional to the recorded intensity. The units of the horizontal axis are the distance center-to-center between contiguous pixels, otherwise known as pixel pitch. In typical digital imaging sensors the pixels are layed out in a rectangular grid, so pixel pitch is the same horizontally and vertically. When dealing with units, pixel pitch is often shortened to ‘pixel’, as shown below.

which of course would be equivalent to 2659 lw/ph. The figures are not identical because of slight inaccuracies in the information. The earlier figures rely on the D800e’s pixel pitch being exactly 4.80um and its usable sensor height being exactly 24.0mm, either of which dimension could be slightly off. The latter figures for picture height are the more precise of the two because they rely only on the number of effective image pixels available for display, which is an accurately known number.

Line pairs per mmcalculator

Hi jack, Thanks for your reply . I am not exactly sure what a pixel is in my case and I am not using an MTF mapper. I have a digital X-Ray. I draw a line from a bone to a dark region thus moving from an area of high attenuation to an area of low attenuation. Attenuation value samples are taken every 0.05 mm on that line. These attenuation values are differentiated to get a nice gaussian distribution as expected. On the xaxis I have the number of samples. Then fft. When I plot the values of fft on matlab I get a nice mtf curve as expected but the xaxis values are still samples starting from 0 to N where N = (length of initial line)/0.05. I want the x axis to show line pairs per mm and not samples. So basically my question is how to convert from number of samples to lp/mm. Thanks in advance.

The ESF of a non-existent perfect imaging system should be recorded as a step function in the raw data, with an instantaneous transition from minimum to maximum occurring at the origin. However, blurring introduced by the physical hardware (lens pupil size and aberrations, filter stack, effective pixel aperture and how ‘sharp’ the physical edge is itself) spreads the step out to a monotonically increasing stretched S shape as shown above. The shorter the rise in pixels, the closer the performance of the lens/camera combination to a perfect imaging system, the better the resulting image ‘sharpness’. As a first approximation we could arbitrarily say that this lens/sensor/target combination produces the image of an edge on the sensor which rises from 10% to 90% intensity within the space of a couple of pixels (center-to-center = pixel pitch).

Several sites for photographers perform spatial resolution ‘sharpness’ testing of a specific lens and digital camera set up by capturing a target. You can also measure your own equipment relatively easily to determine how sharp your hardware is. However comparing results from site to site and to your own can be difficult and/or misleading, starting from the multiplicity of units used: cycles/pixel, line pairs/mm, line widths/picture height, line pairs/image height, cycles/picture height etc.

By taking the differential of the ESF we obtain a Line Spread Function (LSF), equivalent to the one dimensional intensity profile in the direction perpendicular to the edge that a distant, perfectly thin white line against a black background would project on the imaging plane, as captured in the raw data. If obtained carefully and accurately, the LSF is effectively the projection in one dimension of the two dimensional Point Spread Function (PSF). This is what makes the math work (more on the theory behind it here).

Right Wolfgang, pretend the signal is continuous and pixels sample it, if that helps you. In fact these plots were obtained through the Slanted Edge Method, which results in super-resolution (hundreds of samples per pixel). You can read up on it in the relative article, via the link in the third paragraph.

Generally, on a camera lens there is an indication of focal length. For a product name such as “28-75mm F/2.8, ” this “xx mm” indicates the focal length. There are two types of lenses: prime lenses which have a single focal length, and zoom lenses that have a variable focal length. If the focal length is described with a range, such as “xx-xx mm,” it is a zoom lens. For a prime lens, only a single figure is indicated, such as “xx mm.” Example of a zoom lens: 28-75mm F/2.8 Di III VXD G2 (Model A063)Example of a prime lens: 20mm F/2.8 Di III OSD M1:2 (Model F050)

lp/mm calculator

The 17-50mm F/4 Di III VXD (Model A068)It's the world’s first lens covering from ultra wide-angle 17mm to the standard 50mm focal length. The highly-compact TAMRON 17-50mm F/4 Di III VXD (model a068) for Sony E-mount full-frame mirrorless cameras offers maximum versatility for still and video creators. From landscapes to living rooms, this lens captures all that you see.

Units of line pairs per picture height are useful when comparing the performance of two imaging systems apples-to-apples with the final image viewed at the same size. Picture Height (ph) is used interchangeably with Image Height (ih).

‘Lines’ here refers to identical white bars printed on a dark background, separated by spaces equal to their width. So when Kingslake and his cohorts talk about lines per mm they are referring to the number of bars and related spaces within a millimeter. Since the width of the bars and the width of the spaces that separate them are the same, one cycle is equal to two line widths. It makes a difference whether the lines are more square or sinusoidal, but to a first approximation the ‘lines’ of old and the line pairs described in this article can be assimilated (see for instance Lenses in Photography: The Practical Guide to Optics for Photographers, Rudolf Kingslake, Case-Hoyt Corporation, 1951).

The focal length of a lens is defined as the distance from the center of the lens (principal point) to the image sensor of the camera. Focal length is an important figure that determines the angle of view. A lens with a short focal length is a wide-angle lens, a lens with a long focal length is a telephoto lens and a standard lens is somewhere in between. When choosing a lens, pay attention to the focal length and select a lens that suits the subject or scene you want to photograph.

The important point about focal length is that the angle of view changes with its actual number. The angle of view is the angle of area captured by the camera through the lens, and the larger the angel of view, the wider the area is captured. Lens types can be roughly divided into three categories: wide-angle, standard, and telephoto. A standard lens can capture images at an angle of view close to that of the human field of view. Generally, lenses with a wider angle of view are called wide-angle lenses, and lenses with a narrower angle of view are called telephoto lenses. As a general rule of thumb for focal lengths, focal length smaller than 35mm are generally classified into wide-angle lens, lenses around 50mm are called standard lens, and lenses larger than 80mm are telephoto lens. Check out the differences in impression and composition caused by changing the angle of view. Here is an example of a portrait taken with the TAMRON 35-150mm F/2-2.8 Di III VXD (Model A058) at a different focal length. At the wide-angle end (35 mm), the beautiful impression of the figure standing stands out with the background. At the telephoto end (150 mm), on the other hand, the expression on the person's face is compelling and the background bokeh accentuates this image. In this way, by changing the focal length of a zoom lens, various angles of view can be created, and different impressions can be captured.

Concerning the function diagrams – what does the fragmentation of pixels mean? To me a pixel is a unit which can not be subdivided. So I wonder how a smooth function based on units on a quantitative scale(pixesl) can be constructed.

But in practice, do 110lp/mm in the center of the small sensor of an RX100III capture represent better spatial resolution IQ (aka ‘sharpness’) in final images viewed at the same size than 56.3lp/mm in the center of a Full Frame D800e capture?

In addition to the focal length, the F-number (aperture value) is another important figure that expresses the characteristics of the lens: the smaller the F-number, the more light-gathering power it will have, and will broaden your possibility. The F-number is calculated as 'focal length ÷ lens effective diameter'. The smaller the 'maximum aperture F value' when the aperture is at its widest, the more sensitive the lens is. When choosing a lens, it is better to mind the F-number as well as the focal length.

Wide-angle zoom lenses cover the range from ultra wide-angle to standard range. Ultra wide-angle lenses allow you to get closer to buildings and vehicles and still capture a wide range of subjects, resulting in more dynamic shots. It also allows for unique portrait and pet photography, making the most of the perspective. Lightweight and compact TAMRON lenses are particularly useful when shooting landscapes, as the time and distance spent carrying them around can be long.

The loss of contrast at decreasing spatial separation – or inversely at increasing spatial frequency – is what the slanted edge method measures objectively and quantitatively for a given target and imaging system set up in one go. It is able to achieve this feat because an edge is ideally a step function and as we know a step function is made up of all frequencies at once.

Here is some basic knowledge about focal length with interchangeable lenses that you will need to know when shooting with an SLR or mirrorless SLR camera. When shooting with an interchangeable lens camera, you can take beautiful and impressive photos by working with the angle of view, focus point and degree of bokeh. Particularly when choosing a lens, it is important to understand the characteristics of focal length as the angle of view changes depending on focal length. Let’s learn the basic knowledge and make use of it to take the photos as you imagine.

CCD Calculators Useful calculators and formulae. CCD Resolution Calculator. Calculate the resoution in arc seconds per pixel of a CCD with a particular ...

Line pairs per mmconverter

You said a step function contains all frequencies at once. From my audio days many years ago I seem to recall that a square wave has all the odd harmonics and a sawtooth wave has all the evens.

Clearly the resulting intensity swing from brightest point to darkest point in between the two lines changes depending on how much their line spread functions overlap. This relative intensity swing is called Michelson Contrast and it is directly related to our ability to see detail in the image. If no contrast is lost at a specific line spacing (spatial frequency) it means that our imaging system is able to transfer the full intensity swings present in the scene to the raw data. If on the other hand all contrast is lost (that is our imaging system is only able to record a uniform intensity where originally there was contrast) it means that no spatial resolution information from the scene was captured at that spatial separation/frequency.

The profile of the intensity of light reflected by the edge, rotated so that it is perfectly vertical, is shown below. Refer to the earlier link if you are interested in understanding how the ESF can be generated to that level of precision (key word = super-sampling).

A perfect imaging system and target would record the profile of the line as a spike of vertical intensity at zero pixels only. In practice that’s physically impossible but clearly the narrower the LSF is spread out in terms of pixels the better its performance. In this case we could arbitrarily say for instance that one ‘line’ fits within about five pixels, from dark to bright to dark again. Or we could measure the LSF’s full width at half maximum (FWHM) at 1.7 pixels.

Therefore by taking the Fourier Transform of the LSF as determined above and computing its normalized absolute magnitude (modulus) we obtain the contrast transfer function of the target plus imaging system in the direction perpendicular to the edge – this is commonly known as its Modulation Transfer Function (MTF). We take the modulus because MTF is only concerned with the absolute energy present at each spatial frequency, ignoring any phase shifts associated with it.

Of course not. The D800e’s bigger sensor (24mm on the short side) will be able to fit more line pairs along its height than the smaller RX100III’s (8.8mm on the short side). More line pairs in a displayed image viewed at the same size in the same conditions mean better observed spatial resolution. Watch again how the units cancel out to yield line pairs per picture height (lp/ph):

If we have additional physical information, for instance how far pixels are apart or how many usable pixels there are in the sensor – and we typically do – we can easily convert cycles per pixel pitch into some other useful spatial resolution unit often seen in photography. For instance the D800e sensor’s pixel pitch is around 4.8um, so 0.27cycles/pixel from the above MTF50 reading would correspond to 56.3 cycles/mm on the sensor as captured by the given imaging system:

In addition some current sensors have anti-aliasing filters active in one direction only, so that MTF can be quite different in one direction versus its perpendicular. In such cases if the captured detail is not aligned with either direction the spatial resolution performance of the system will vary sinusoidally from maximum to minimum depending on the relative angle of the detail to the strength of the AA. With a one-directional AA the manufacturer is counting on the fact that detail in natural scenes is typically not all aligned in the same direction so the effective resolution tends to average itself out – though this is often not the case with man-made subjects.