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MTF(v) = Mi / M0 A lens system may behave differently depending on the nature of the optical information that passes through it. For example, lens systems vary as a function of the spatial frequency of the stimuli that they handle. You undoubtedly noticed, above, that MTF has spatial frequency (v) as a parameter. Click on image modulation as a function of spatial frequency to see a graphical illustration of how the transfer function of a lens effects the image modulation. Table of Contents  Subject Index  Table of Contents [When not using framtes]

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Olympus and Panasonic Lumix are the most prominent manufacturers using this sensor format. In practice, there can be very slight variations in the dimensions of the sensors from model to model.

modulation = (Lmax - Lmin ) / (Lmax + Lmin) where Lmax is the maximum luminance of the grating and Lmin is the minimum. When modulation is defined in terms of light it is frequently referred to as Michelson contrast. Indeed when one takes the ratio of the illumination from the light and dark bars one is measuring contrast. Now, let's assume that you have a square wave grating of a specific frequency (v) and modulation (contrast) and this stimulus is passed through a lens. The modulation of the image can now be measured. The modulation transfer function (MTF) is defined as the modulation, Mi, of the image divided by the modulation of the stimulus ( the object), Mo, as shown in the following equation. MTF(v) = Mi / M0 A lens system may behave differently depending on the nature of the optical information that passes through it. For example, lens systems vary as a function of the spatial frequency of the stimuli that they handle. You undoubtedly noticed, above, that MTF has spatial frequency (v) as a parameter. Click on image modulation as a function of spatial frequency to see a graphical illustration of how the transfer function of a lens effects the image modulation. Table of Contents  Subject Index  Table of Contents [When not using framtes]

The reason I’ve singled Canon out as a special case here is that Canon’s APS-C sensors are just a smidgeon smaller than most other APS-C sensors.

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Yes, this angle-of-view calculator works for zoom and prime lenses. You can enter any single, specific focal length along the zoom range. For instance, for a 24-70mm zoom lens, you can enter 55mm to see the angle of view at that point in the zoom range.

Now, let's assume that you have a square wave grating of a specific frequency (v) and modulation (contrast) and this stimulus is passed through a lens. The modulation of the image can now be measured. The modulation transfer function (MTF) is defined as the modulation, Mi, of the image divided by the modulation of the stimulus ( the object), Mo, as shown in the following equation. MTF(v) = Mi / M0 A lens system may behave differently depending on the nature of the optical information that passes through it. For example, lens systems vary as a function of the spatial frequency of the stimuli that they handle. You undoubtedly noticed, above, that MTF has spatial frequency (v) as a parameter. Click on image modulation as a function of spatial frequency to see a graphical illustration of how the transfer function of a lens effects the image modulation. Table of Contents  Subject Index  Table of Contents [When not using framtes]

The same general principles apply for film, but instead of using the size of the sensor you’d use the size of the exposed film plane.

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Here’s a calculator for the angles of view from lenses on digital camera sensors, as well as angle of view charts for common focal lengths. And I’ve also included an explanation of why the diagonal angle of view matters more than you might think.

It’s also a fixed reference point if you’re using the same or similar focal lengths but on different-sized sensors. For instance, a 20mm lens will give you a wider angle of view on a full-frame camera than on a Micro Four Thirds camera.

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That’s because it’s the spec that lens manufacturers include in their spec sheets. So when you see that a lens has so-and-so degrees angle of view, it’s actually telling you it’s from one corner to the diagonally opposite corner. It’s not telling you the angle of view from side to side. In that respect, it’s a bit like the size spec that TV manufacturers use (i.e., a 55-inch TV is 55 inches from one corner to the diagonal corner, not from one side to the other side).

When you see that a lens has so-and-so degrees angle of view, it’s actually telling you it’s from one corner to the diagonally opposite corner. It’s not telling you the angle of view from side to side.

Recall in a square wave grating there were dark bars and light bars. We can measure the amount of light coming from each. The maximum amount of light will come from the light and the minimum from the dark bars. If the light is measured in terms of luminance (L) we can define modulation according to the following equation: modulation = (Lmax - Lmin ) / (Lmax + Lmin) where Lmax is the maximum luminance of the grating and Lmin is the minimum. When modulation is defined in terms of light it is frequently referred to as Michelson contrast. Indeed when one takes the ratio of the illumination from the light and dark bars one is measuring contrast. Now, let's assume that you have a square wave grating of a specific frequency (v) and modulation (contrast) and this stimulus is passed through a lens. The modulation of the image can now be measured. The modulation transfer function (MTF) is defined as the modulation, Mi, of the image divided by the modulation of the stimulus ( the object), Mo, as shown in the following equation. MTF(v) = Mi / M0 A lens system may behave differently depending on the nature of the optical information that passes through it. For example, lens systems vary as a function of the spatial frequency of the stimuli that they handle. You undoubtedly noticed, above, that MTF has spatial frequency (v) as a parameter. Click on image modulation as a function of spatial frequency to see a graphical illustration of how the transfer function of a lens effects the image modulation. Table of Contents  Subject Index  Table of Contents [When not using framtes]

An easy example is when shooting architecture or landscapes. For those, you often might want to be able to fit quite a wide perspective, or large angle of view, in the frame.

My name is David Coleman, and this is my site. I take photos for a living. Seven continents. Dozens of countries. Up mountains. Under water. And a bunch of places in between. I'm based in Washington DC.

Most lenses including the human lens are not perfect optical systems. As a result when visual stimuli are passed through them they undergo a certain degree of degradation. The question is how can this degradation be evaluated? Before we can answer this question we need to define "modulation." Recall in a square wave grating there were dark bars and light bars. We can measure the amount of light coming from each. The maximum amount of light will come from the light and the minimum from the dark bars. If the light is measured in terms of luminance (L) we can define modulation according to the following equation: modulation = (Lmax - Lmin ) / (Lmax + Lmin) where Lmax is the maximum luminance of the grating and Lmin is the minimum. When modulation is defined in terms of light it is frequently referred to as Michelson contrast. Indeed when one takes the ratio of the illumination from the light and dark bars one is measuring contrast. Now, let's assume that you have a square wave grating of a specific frequency (v) and modulation (contrast) and this stimulus is passed through a lens. The modulation of the image can now be measured. The modulation transfer function (MTF) is defined as the modulation, Mi, of the image divided by the modulation of the stimulus ( the object), Mo, as shown in the following equation. MTF(v) = Mi / M0 A lens system may behave differently depending on the nature of the optical information that passes through it. For example, lens systems vary as a function of the spatial frequency of the stimuli that they handle. You undoubtedly noticed, above, that MTF has spatial frequency (v) as a parameter. Click on image modulation as a function of spatial frequency to see a graphical illustration of how the transfer function of a lens effects the image modulation. Table of Contents  Subject Index  Table of Contents [When not using framtes]

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For 35mm film, that’s going to be functionally the same as using the full-frame option in the calculator above. I haven’t added other film sizes, but I might try to put together a separate calculator for that.

The data here is calculated. For more specific data that applies to a particular model of lens, check the manufacturer’s spec sheets for that lens. Sometimes there might be, say, a half degree of variation, but in general, these rounded numbers should get you very close. I’ve compared them with a number of lens spec sheets and found the data here to be quite accurate.

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This is for full-frame digital cameras with a sensor that measures 36mm x 24mm, which is the convention for a full-frame sensor. It also applies to SLR cameras using 35mm film.

The practical angle of view of a lens varies based on the camera’s sensor size, so I’ve included some of the most common sensor sizes.

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The modulation transfer function (MTF) is defined as the modulation, Mi, of the image divided by the modulation of the stimulus ( the object), Mo, as shown in the following equation. MTF(v) = Mi / M0 A lens system may behave differently depending on the nature of the optical information that passes through it. For example, lens systems vary as a function of the spatial frequency of the stimuli that they handle. You undoubtedly noticed, above, that MTF has spatial frequency (v) as a parameter. Click on image modulation as a function of spatial frequency to see a graphical illustration of how the transfer function of a lens effects the image modulation. Table of Contents  Subject Index  Table of Contents [When not using framtes]

By having a reference point you can compare lenses in an apples-to-apples kind of way. That can be very handy when choosing the right lens for the job.

These charts offer an alternative way of visualizing the calculated data above. It might be useful if you’re approaching it from the other direction and trying to find a lens that has a particular visual coverage that you’re after.

When you’re taking photos, the angles of view horizontally or laterally across the frame or vertically up and down the frame are probably the ones you’re most focused on. But it’s actually the diagonal measurement that comes up more often.

Image

Knowing the angle of view gives you a baseline reference for how wide a perspective you can fit in the frame. In a practical sense, I find it useful for choosing which lens is right for the job.

A larger angle of view corresponds to a wider lens, meaning you can fit more perspective within the frame. Conversely, a smaller angle of view gives you a narrow perspective, as you might get with a telephoto lens.