表示对这个函数求导
表示这个函数的导数
比如 lnx`＝1/x
或者你要的是这个答案：
The size of pinhole you need depends on the kind of effect you want to get. Many of us calculate the "optimum" size and then depart (or not) from it, in order to experiment. There are many formulas to calculate the "optimum" size. Optimum, in this case, means the hole that gives us the "sharpest" pictures. Incidentally, the sharpest pictures may or may not be the "best" pictures for you. The formula I use is:
where Pinhole Diameter and focal length are expresses in inches
where Pinhole Diameter and focal length are expresses in millimeters
Once you know the size of the pinhole aperture you will need, find the f/stop of your camera by dividing the focal length or distance pinhole to film plane by the diameter. Obviously, both values must be expressed in the same units.
More likely than not, the f/stop won't coincide with a full stop. Since the progression of f/stops is not linear, you would need a math formula to find where exactly in between full stops the f/stop of your pinhole camera is, but due to the "imprecise" nature of the pinhole practice, that is not really necessary (for some the more imprecise the better, some others want it imprecise but controlled to certain extent, others want to know how to make it precise so they depart from that precision and others like it very precise, period! No pinhole practicioners in the latter category though!).
I would suggest you approximate the calculated f/stop to the next full stop (unless is really close to lower one). The reason is that, pinhole exposures are more likely to be under than over exposed. Once you know the full f/stop of your camera, it's time to make some pictures. You then have to find the exposure your scene needs. Do it by whatever method you want. I use 2 methods. The first is by applying the "Sunny16" rule, which says that under sunny/bright conditions the exposure needed is f/16 and 1 / (ISO film speed). For instance, if the film is ISO100 the exposure needed would be f/16 and 1/100 secs. The second method is taking an actual light reading of the scene. Sometimes I use a handheld meter, other times I use my 35mm camera metering system.
I want to state at this point that exposure in photography is given by a pair of values, they are the aperture or f/stop and the exposure time, let's call then "f" and "t" respectively (we will use this letters later).
Once you have the exposure that your scene needs, by means of "Sunny16" rule or taking an actual reading with a light meter or camera, you have to find the equivalent exposure values for when the f/stop is the one of your pinhole camera. Let's call this new pair of exposure values "F" and "T", respectively (notice they are upper case letters and that "F" is the actual f/stop of your pinhole camera). You then start to double "f" until you get a value that is equal or bigger than "F". If equal, the number of doublings multiplied by 2 is the number of f/stops separating "f" from "F". If bigger, the number of f/stops between "f" and "F" is the number of doublings times 2 minus 1. The new exposure time ("T") will be obtained by doubling the time "t" as many times as stops separate "f" from "F". It is more difficult and cumbersome to say or write it, than to actually do it.
Let's use an example, let's assume we have a 6" focal length camera, we are shooting under bright sunny open skies and that we are using B&W paper as our "film". Let's mention here that B&W paper has an average equivalent to film speed of ISO-6:
f/stop progression from f/16 to above f/333 is :
Actual f/stop of pinhole camera is f/333. Next full f/stop above it is f/360. Therefore, the practical f/stop of the pinhole camera should be = f/360
Scene to photograph is under sunny conditions, material used as negative is B&W multigrade paper. Approximate ISO speed for it is ISO6. Therefore, using Sunny16 we should expose for 1/6 secs @ f/16.
As per the f/stop progression table above, there are 9 stops separating f/16 and our camera practical f/stop of f/360
Since our camera aperture is 9 stops smaller than f/16, we then have to double 9 times the exposure time of 1/6 seconds:
1/6 => 1/3 1/1.5 1.33 2.66 5.33 10.66 21.33 42.66 85.33
The exposure time for when aperture is f/352 should be = 85 seconds.
In other words: The equivalent exposure time to f/16 and 1/6sec is f/352 and 85 seconds.
Unfortunately this is not the end of it, anytime we have an exposure longer than 1 second we have to apply reciprocity failure corrections. For film, you can refer to the information provided together with the film you are using or refer to the Web Site of the film manufacturer. If you are using B&W paper as your negative material, the following table has proven very effective for me.
1" 1.25
5" 1.5
10" 1.75
25" 2
40" 2.4
1' 2.75
2' 3
5' 4
10' 5
20' 6
The first column is the uncorrected time, the second one is the factor by which we have to multiply the uncorrected time to obtain our reciprocity corrected time.
In our example, the 85 seconds are about 1.5 minutes. The factor would be between 2.75 and 3. Let's select 3 as the multiplier. The new reciprocity corrected time would then be 4.5 minutes. In conclusion, we have translated our "sunny/16" determined exposure of f/16 and 1/6 secs to a non-reciprocity corrected exposure of f/352 and 85 secs and then to a reciprocity corrected exposure of f/352 and 4.5 minutes.
When shooting outdoors, you have to watch for changing light conditions during long exposures as you may have to adjust the exposure time a little bit to compensate for those changing conditions. When I was making DOOR (using B&W paper as negative material), the uncorrected exposure time was 8 minutes. The multiplier according to the table above is 5 for total corrected time of 40 minutes! A big cloud passed by during part of the 40 minutes, that made me extend the exposure time to 55 minutes to compensate. During this time, I also exposed my body for 55 minutes to 19 degrees bellow the freezing mark!