Another application of the trick of adding a clause with an always failing guard Reversing Haskell typechecker: We get the real function, which we can then apply to various arguments. Informally, we converted from undefined to defined.
Same Display Dimensions As a corollary, Equivalent lenses are lenses that produce Equivalent photos on the format they are used on which means they will have the same AOV angle of view and the same aperture diameter.
The focal lengths all have the same [diagonal] AOVso we say the focal lengths are equivalent. The same total amount of light falls on the sensor for the same equivalent relative aperture and same exposure time, so we say the exposures are equivalent.
The photos will have the same lightness for the same equivalent how to write an equivalence class and equivalent ISO setting, so we say the ISO settings are equivalent. An important consequence of the same aperture entrance pupil diameter is that the DOF and diffraction will also be the same for a given perspective, framing, display size, viewing distance, and visual acuity.
In addition, since the exposure times are the same, the same total amount of light will fall on the sensor for all systems with a given scene luminance how to write an equivalence class lens transmissionwhich means the photos will have the same noise if the sensors are equally efficient.
Of course, sensors are not equally efficient although often, but not always, close for a given generationnor are all lenses proportionally sharp, have the same color, bokeh, distortion, or flare characteristics, nor do all sensors have the same pixel count, CFA, and AA filter.
Indeed, according to Webster'sthe primary definition of "equivalent" is: Equality of other visual properties, such as noise, detail, etc. The second and third definitions of "equivalent" also fits: On the other hand, sensors of the same generation are usually pretty close in terms of efficiency see here for quite a few examples.
Still, there are other issues to consider, such as color and distortion although these two can usually be corrected for in processingbokeh, lens flare, etc. So while differences in the technology may well make for differences that matter more than one or more of the parameters of Equivalence, Equivalent photos will typically be the closest in appearance more so, of course, when the sensors are of the same generation.
The larger the photo is displayed, the more extreme the processing, and the lower the amount of light that makes up the photo, the more obvious the role that differences in technology will play.
In addition, there is a small niggle in the parameter of "same framing" for systems with different aspect ratios e. We can either crop one image to the the aspect ratio of the other or crop both to a common aspect ratio or compare at the same AOV and display with the same diagonal measurement.
The details of this are discussed at the end of this section.
It is important to note that Equivalent photos on different formats will not have the same exposureand this is the source of most all resistance to the concept. The reason is quite simple: The same total amount of light will fall on the sensor for Equivalent photos which results in a lower density of light exposure on a larger sensor.
Many feel that exposure has been usurped with DOFbut this reflects not only a lack of understanding of what exposure actually is, but how much of a role DOF plays in a photo, even if DOF, per se, is not a consideration.
While the artistic value of DOF is subjective, the fact is that both the total light falling on the sensor and the DOF are functions of the aperture diameter. Larger aperture diameters admit more light, but they also introduce more aberrations from the lens.
Thus, DOF, noise, and sharpness are all intrinsically related through the aperture of the lens. Exposure is not how bright or dark a photo appears -- we can lighten or darken a photo as we see fit. However, it is not the density of light falling on the sensor that matters, but the total light photons that makes up the photo, since the total light, combined with the sensor efficiency, determine the image noise.
This crucial distinction between exposure and total light has an entire section of the essay devoted to it, as does the section on noise. So, while equal noise is not a parameter of Equivalent images, it is a consequence of Equivalent images if the sensors are equally efficient. The primary elements in image noise, in order, are: People commonly believe that larger sensor systems have less relative noise because they have better sensors, when, in fact, it is instead because they collect more total light for a given exposure.
Thus, breaking the properties of Equivalence down into the properties of the photo, lens, and sensor: If photos are taken of the same scene from the same position with the same focal point, have the same framing, same display dimensions, and same aperture diameter, they will have the same DOF and diffraction.
If the sensors record the same proportion of light falling on them same QE and add in the same electronic noise the noise from the sensor and supporting hardwarethen the noise will be the same regardless of pixel count and ISO setting keeping in mind that sensors of the same, or nearly the same, generation typically record very nearly the same proportion of light falling on them regardless of brand, size, or pixel count a notable exception would be BSI tech which records a third to half a stop more light for a given exposure than non-BSI tech and that the electronic noise matters only for the portions of the photo made with very little light.
If the lenses resolve proportionally the same on their respective sensors at the same DOF e. Note that it said above that "equivalent images on different formats will usually have the most similar visual properties" -- but not always.
Or, if the extreme corners are of some importance in the composition, and one system has greater edge sharpness than the other, the system with the softer edges may need to stop down more to achieve sharper corners.
But, in most circumstances, Equivalent images will be, if not the most similar, very close. A competent photographer will use their equipment to obtain the best image possible, which often means trading one IQ component for another for example, when using a wider aperture to get less noise at the expense of less sharpness and greater vignetting.
However, it is important that we understand that these compromises represent choices that a photographer makes, and are not requirements imposed by the format.
Extending the example, it is disingenuous to say that a smaller format is superior to a larger format because it has more DOF, or is sharper, "wide open" than the larger format, when "wide open" is a choice, not a mandate, that results in a different sometimes radically different DOF and relative noise, and the larger format can simply be stopped down for greater DOF and sharpness although, if stopping down requires a concomitant increase in ISO to maintain a sufficient shutter speed, then the larger format may have to sacrifice some, or even all, of its noise advantage.
Thus, Equivalence is about the consequences of choices a photographer has in terms of IQ as a function of format. Understanding the fundamental concepts of Equivalence requires making important distinctions between various terms which people often take to mean the same thing. It is very much akin to making the distinction between "mass" and "weight", two terms which most people take to mean the same thing, when, in fact, they measure two different but related quantities.
While there are circumstances where making the distinction is unnecessary, there are other times when it is critical. The first of these distinctions that needs to be made is between aperture and f-ratio.Search the world's information, including webpages, images, videos and more.
Google has many special features to help you find exactly what you're looking for. For a, b ∈ S we will write a b,not Comment: Later we will begin to treat an equivalence class as a single mathematical object (rather than view it as a set).
For example, in certain circumstances we will add and multiply equivalence classes.
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