Misplaced Pages

#460539

30-456: Double exposure is the outcome of overlaying an image on a previously exposed film, either deliberately or accidentally. Double exposure may also refer to: Double exposure Ordinarily, cameras have a sensitivity to light that is a function of time. For example, a one-second exposure is an exposure in which the camera image is equally responsive to light over the exposure time of one second. The criterion for determining that something

60-511: A film scanner for increasing dynamic range . With multiple exposure the original gets scanned several times with different exposure intensities. An overexposed scan lights the shadow areas of the image and enables the scanner to capture more image information here. Afterwards the data can be calculated into a single HDR image with increased dynamic range. Among the scanning software solutions which implement multiple exposure are VueScan and SilverFast . Exponential decay A quantity

90-417: A well-known expected value . We can compute it here using integration by parts . A quantity may decay via two or more different processes simultaneously. In general, these processes (often called "decay modes", "decay channels", "decay routes" etc.) have different probabilities of occurring, and thus occur at different rates with different half-lives, in parallel. The total decay rate of the quantity  N

120-500: A constant factor, the same equation holds in terms of the two corresponding half-lives: where T 1 / 2 {\displaystyle T_{1/2}} is the combined or total half-life for the process, t 1 {\displaystyle t_{1}} and t 2 {\displaystyle t_{2}} are so-named partial half-lives of corresponding processes. Terms "partial half-life" and "partial mean life" denote quantities derived from

150-524: A constant finite rectangular window, in combination. For example, a sensitivity window comprising a Dirac comb combined with a rectangular pulse, is considered a multiple exposure, even though the sensitivity never goes to zero during the exposure. In the historical technique of chronophotography, dating back to the Victorian era , a series of instantaneous photographs were taken at short and equal intervals of time. These photographs could be overlayed for

180-437: A decay constant as if the given decay mode were the only decay mode for the quantity. The term "partial half-life" is misleading, because it cannot be measured as a time interval for which a certain quantity is halved . In terms of separate decay constants, the total half-life T 1 / 2 {\displaystyle T_{1/2}} can be shown to be For a decay by three simultaneous exponential processes

210-472: A lit subject in two (or more) different positions against a perfectly dark background, as the background area will be essentially unexposed. Medium to low light is ideal for double exposures. A tripod may not be necessary if combining different scenes in one shot. In some conditions, for example, recording the whole progress of a lunar eclipse in multiple exposures, a stable tripod is essential. More than two exposures can be combined, with care not to overexpose

240-400: A mean lifetime of 200 days. The equation that describes exponential decay is or, by rearranging (applying the technique called separation of variables ), Integrating, we have where C is the constant of integration , and hence where the final substitution, N 0 = e , is obtained by evaluating the equation at t = 0, as N 0 is defined as being the quantity at t = 0. This

270-421: A multiple exposure feature can be set to double-expose after making the first exposure. Since shooting multiple exposures will expose the same frame multiple times, negative exposure compensation must first be set to avoid overexposure. For example, to expose the frame twice with correct exposure, a −1 EV compensation have to be done, and −2 EV for exposing four times. This may not be necessary when photographing

300-435: A scene that were not originally there. It is frequently used in photographic hoaxes . It is considered easiest to have a manual winding camera for double exposures. On automatic winding cameras, as soon as a picture is taken the film is typically wound to the next frame. Some more advanced automatic winding cameras have the option for multiple exposures but it must be set before making each exposure. Manual winding cameras with

330-442: A single multiple exposure print. In photography and cinematography , multiple exposure is a technique in which the camera shutter is opened more than once to expose the film multiple times, usually to different images. The resulting image contains the subsequent image/s superimposed over the original. The technique is sometimes used as an artistic visual effect and can be used to create ghostly images or to add people and objects to

SECTION 10

#1732790222461

360-468: A time-windowing function, such as a Gaussian, that weights time periods near the center of the exposure time more strongly. Another possibility for synthesizing long exposure from a multiple exposure is to use an exponential decay in which the current frame has the strongest weight, and previous frames are faded out with a sliding exponential window. Multiple exposure technique can also be used when scanning transparencies like slides, film or negatives using

390-402: Is 2  = 1/2 raised to the (whole or fractional) number of half-lives that have passed. Thus, after 3 half-lives there will be 1/2  = 1/8 of the original material left. Therefore, the mean lifetime τ {\displaystyle \tau } is equal to the half-life divided by the natural log of 2, or: For example, polonium-210 has a half-life of 138 days, and

420-417: Is 368. A very similar equation will be seen below, which arises when the base of the exponential is chosen to be 2, rather than e . In that case the scaling time is the "half-life". A more intuitive characteristic of exponential decay for many people is the time required for the decaying quantity to fall to one half of its initial value. (If N ( t ) is discrete, then this is the median life-time rather than

450-413: Is a double exposure is that the sensitivity goes up and then back down. The simplest example of a multiple exposure is a double exposure without flash, i.e. two partial exposures are made and then combined into one complete exposure. Some single exposures, such as "flash and blur" use a combination of electronic flash and ambient exposure. This effect can be approximated by a Dirac delta measure (flash) and

480-464: Is by definition the multiplicative inverse of corresponding partial decay constant: τ = 1 / λ {\displaystyle \tau =1/\lambda } . A combined τ c {\displaystyle \tau _{c}} can be given in terms of λ {\displaystyle \lambda } s: Since half-lives differ from mean life τ {\displaystyle \tau } by

510-466: Is given by the sum of the decay routes; thus, in the case of two processes: The solution to this equation is given in the previous section, where the sum of λ 1 + λ 2 {\displaystyle \lambda _{1}+\lambda _{2}\,} is treated as a new total decay constant λ c {\displaystyle \lambda _{c}} . Partial mean life associated with individual processes

540-444: Is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation , where N is the quantity and λ ( lambda ) is a positive rate called the exponential decay constant , disintegration constant , rate constant , or transformation constant : The solution to this equation (see derivation below) is: where N ( t )

570-426: Is the form of the equation that is most commonly used to describe exponential decay. Any one of decay constant, mean lifetime, or half-life is sufficient to characterise the decay. The notation λ for the decay constant is a remnant of the usual notation for an eigenvalue . In this case, λ is the eigenvalue of the negative of the differential operator with N ( t ) as the corresponding eigenfunction . The units of

600-471: Is the quantity at time t , N 0 = N (0) is the initial quantity, that is, the quantity at time t = 0 . If the decaying quantity, N ( t ), is the number of discrete elements in a certain set , it is possible to compute the average length of time that an element remains in the set. This is called the mean lifetime (or simply the lifetime ), where the exponential time constant , τ {\displaystyle \tau } , relates to

630-463: The assembly is reduced to 1 ⁄ e ≈ 0.367879441 times its initial value. This is equivalent to log 2 ⁡ e {\displaystyle \log _{2}{e}} ≈ 1.442695 half-lives. For example, if the initial population of the assembly, N (0), is 1000, then the population at time τ {\displaystyle \tau } , N ( τ ) {\displaystyle N(\tau )} ,

SECTION 20

#1732790222461

660-435: The body by a process reasonably modeled as exponential decay, or might be deliberately formulated to have such a release profile. Exponential decay occurs in a wide variety of situations. Most of these fall into the domain of the natural sciences . Many decay processes that are often treated as exponential, are really only exponential so long as the sample is large and the law of large numbers holds. For small samples,

690-445: The decay constant are s . Given an assembly of elements, the number of which decreases ultimately to zero, the mean lifetime , τ {\displaystyle \tau } , (also called simply the lifetime ) is the expected value of the amount of time before an object is removed from the assembly. Specifically, if the individual lifetime of an element of the assembly is the time elapsed between some reference time and

720-403: The decay rate constant, λ, in the following way: The mean lifetime can be looked at as a "scaling time", because the exponential decay equation can be written in terms of the mean lifetime, τ {\displaystyle \tau } , instead of the decay constant, λ: and that τ {\displaystyle \tau } is the time at which the population of

750-520: The film. Digital technology enables images to be superimposed over each other by using a software photo editor , such as Adobe Photoshop or the GIMP . These enable the opacity of the images to be altered and for an image to be overlaid over another. They also can set the layers to multiply mode, which 'adds' the colors together rather than making the colors of either image pale and translucent. Many digital SLR cameras allow multiple exposures to be made on

780-423: The mean life-time.) This time is called the half-life , and often denoted by the symbol t 1/2 . The half-life can be written in terms of the decay constant, or the mean lifetime, as: When this expression is inserted for τ {\displaystyle \tau } in the exponential equation above, and ln 2 is absorbed into the base, this equation becomes: Thus, the amount of material left

810-475: The multiple exposure effect. Examples include Joan Semmel 's oil on canvas "Transitions" from 2012, and Ian Hornak 's acrylic on canvas "Hanna Tillich's Mirror: Rembrandt's Three Trees Transformed Into The Expulsion From Eden", from 1978 (depicted below). With traditional film cameras, a long exposure is a single exposure, whereas with electronic cameras a long exposure can be obtained by integrating together many exposures. This averaging also permits there to be

840-432: The removal of that element from the assembly, the mean lifetime is the arithmetic mean of the individual lifetimes. Starting from the population formula first let c be the normalizing factor to convert to a probability density function : or, on rearranging, Exponential decay is a scalar multiple of the exponential distribution (i.e. the individual lifetime of each object is exponentially distributed), which has

870-449: The same image within the camera without the need for any external software. And some bridge cameras can take successive multiple exposures (sometimes up to nine) in one frame and in one shot. It is the same with high-dynamic-range imaging , which takes multiple shots in one burst captures, then combines all the proper shots into one frame. In addition to direct photographic usage of the technique, fine artists ' work has been inspired by

900-495: The total half-life can be computed as above: In nuclear science and pharmacokinetics , the agent of interest might be situated in a decay chain, where the accumulation is governed by exponential decay of a source agent, while the agent of interest itself decays by means of an exponential process. These systems are solved using the Bateman equation . In the pharmacology setting, some ingested substances might be absorbed into

#460539