Diffractiongratingformula

Another method of measuring the negative lens. Good for thin lens. Simple: A method more complicated for measuring the focal length of negative lens - to make a simple Galilean telescope. No matter if lens is simple or achromat. Originally posted ages ago. (permalink) tamasflex edited this topic ages ago.

Diffractiongratingexperiment

johnny: Thank you for the nice write-up. When measuring the f-stop of certain multi-element lenses, using the camera's meter/imager is not adequate because of differences in light transmission (e.g. number of elements, dispersion, etc.), contrast/flare (e.g. uncoated lenses), fundamental design (e.g. refractors vs. mirrors), can affect the measured reading quite a bit. If say I want to measure the f-stop of a lens to be able to calculate its DOF, what is the best way to do it? I imagine even using an image processing based quantitative focus-defocus analysis between the mystery lens and a reference lens would not be adequate because lens design choices/optimisations can affect the rendering of the same defocu areas differently between the two lenses. Any suggestions? ages ago (permalink)

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The way I measured the length of a negative focal length lens in my physics class was to put it next to a positive focal length lens of known length, then measured the focal length of the two lens system, then figuring out the focal length was just a bit of math math something like 1/f = 1/fknown + 1/funknown ages ago (permalink)

Reflection gratingexamples

Hi Johnny, As for the fact that homemade lenses only have much lower contrast making it hard to compare the histogram with the image from a fully corrected lens, the solution is to use a low or no contrast image as your testI usually get the camera's meter to tell me... saves a lot of trouble with comparing histograms :) As for comparing things, I was talking about measuring the defocus amounts between a reference lens and an unknown lens of the same focal length. Ideally, this can be done by ensuring that both lenses are focused at a certain distance and then quantitatively comparing a defocused area, I imagine. ages ago (permalink)

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The best way I have found to measure the focal length of a positive lens is the f/2f approach. Simply put, focus at infinity, measure from any convenient, repeatable point to the focal plane. Rack the lens out to 1:1, which will be at 2f. Measure from the same reference point to the focal plane. Subtract the first number from the second and the actual focla length is the result. Once you have that number, aperture is trivial. Aperture (in f stop)= focal length divided by entrance pupil diameter. (I can hear you all saying "wtf is the entrance pupil, and more importantly, how do I measure it??") The entrance pupil is the apparent size of the aperture or iris, given the magnification of the front element. There are two easy ways to measure entrance pupil, one will get you a rough estimate (to a mm or so), the other more exact. The first approach, is to hold the lens at arms length, and using a dial or electronic caliper, measure the clear aperture of the lens wide open. This will give you, within a mm or so, the entrance pupil. (this is the approach I use, typically) The second approach, is to illuminate the lens from the rear, (I use a lamp shining into the rear of my view camera with the ground glass removed), hold a piece of matte acetate to the front element and make a couple of pencil marks denoting where the the edge of the illuminate circle is. Measure the distance and that is your entrance pupil dimension. Pretty easy once you get the hang of it, actually. Originally posted ages ago. (permalink) epatsellis edited this topic ages ago.

Transmissiongrating

My teachers and textbooks tend to gloss over this point. Why do reflection gratings work, and why is there not a contradiction with the law of reflection?

What isgrating

All this math makes me panic but I want to make a lens so badly! :( ages ago (permalink)

Homemade Lenses: Measuring Focal Length, Aperture and F-Stop I've been asked how I measure the focal length and f-stop of my homemade lenses. The answer is: That depends. It depends on whether I am measuring a single element lens, in which case there is a simple way to directly measure focal length and f-stop, or I am measuring a multi-element lens, in which case I use a comparison method. Let's take the simple case first. Single element lenses with positive focal lengths, (that is, they focus light, rather than diverge it) can be directly measured to determine their focal lengths and apertures. You'll need a piece of paper, a ruler, and a distant light source such as a lamp across the room (do NOT use the sun for this). Project the light from the lamp through the lens and onto the paper. Adjust the distance between the lens and the paper until the image is at its sharpest. Now just measure the distance from the lens to the image on the paper. This is the focal length of the lens, or close to it. Ideally, the light source should be an infinite distance away, but I find that a light across the room gives me a pretty good approximation. (If you insist on precision, then also measure the distance from the object to the lens and use the formula given below.) The aperture of a single element lens is even easier. Just measure the diameter of the lens, excluding any opaque border or mount. The f-stop (or the term I prefer: focal ratio) is simply the focal length divided by the aperture. Example: Suppose that when you projected a distant light source through a lens and onto a piece of paper, the distance between the lens and the focused image was about 6 inches (150 mm). Suppose also that this lens is about 2 inches (50 mm) in diameter. The focal ratio of the lens is 6 divided by 2 (or 150 divided by 50) which equals f/ 3.0. OK, that was too easy. Multi-element lenses are not that easy. First of all, you cannot determine the focal length of a multi-element lens simply by measuring the distance from the lens to a focused image. Doing that, doesn't tell you the focal length, however it does tell you something interesting. It tells you the back focal length, which is also important because that's where the film/sensor needs to be to capture focused images. But I'm getting off topic. To understand the measurement of focal length, do the following experiment: Take that awful zoom kit lens that came with your camera (or any zoom lens), and starting with the lens set to its shortest focal length, measure the distance from the lens mount to a focused image just as we did above for a single element lens. If the lens was made for a SLR or DSLR, then you will get a measurement in the range of 45 mm. This is the back focal length. Now adjust the zoom to the maximum focal length and take the measurement again. What's this? It doesn't change. But did you notice that something else did change? The size of the image changed. So the key to measuring focal length of a complex lens is to measure the image size. It's possible to do this with an image projected on a piece of paper. But there's a better way: using photographs to compare the image size with a lens of a known focal length. You've probably figured it out by now, but let me spell it out, step-by-step. Put your camera on a tripod and point it at an object with distinct edges. I like to use a bookcase. Now take two photos: one using your mystery lens, and one using a reference lens with a known focal length. If your reference lens is a zoom, try to adjust it so that the object appears to be the same size as it is with the mystery lens. If you are able to get a match, just look at where the zoom is set. That is the focal length of your mystery lens. However, if your mystery lens seems to be outside the range of your zoom, or if you are comparing it to a fixed (prime) lens, then there are a few more steps. Choose the biggest object that is clearly defined in both images. I like to use the distance between two shelves in my bookcase. Get your ruler out again because you will need to measure the size of this object as it appears in each of your two photos. I usually do a crude measurement using the LCD on the back of my camera. A more accurate measurement can be done by uploading them to your computer. Either way, just make sure you are comparing full size images shown at the same size. The focal length of your mystery lens is calculated by multiplying the focal length of your reference lens by the ratio of the two measurements. Example: suppose your reference lens has a focal length of 50 mm. And suppose that when you measure the distance between two shelves in the image taken with the mystery lens you get 35 mm, while in the image taken with the reference lens, the distance between two shelves measures 25 mm. This means that your mystery lens has a focal length of 50 x (35 / 25) = 70 mm. By the way, there's absolutely no reason why the above method can't be used with film. It just won't be as fast. Great, that's focal length. Now what about f-stop? Once again, I find that the most practical way to measure the effective focal ratio of a homemade or mystery lens is by comparing it to a reference lens. Once you've determined the focal length, use a reference lens with a focal length that is as close as possible to your mystery lens. Mount your camera on a tripod and point it at a scene in which the light level is not changing. I generally do this inside, under artificial light. Starting with the mystery lens and the camera set to manual, adjust the shutter speed (and ISO if necessary) to get a correctly exposed photo. Now, leaving the shutter speed and ISO unchanged, try to get a matching photo using your reference lens by adjusting only the aperture. The histogram is very helpful. Keep in mind that if you are testing a homemade lens, it probably has much lower contrast than your reference lens, which will cause your histogram to be "scrunched together." You're looking for an approximate match of the centers of the curves. Just as when we were testing focal length, there are two possible outcomes. If you find an approximate match, you're done. Just read off the f-stop from the reference lens. However, if your mystery lens seems to be outside the aperture range of your reference lens, (most likely faster), then you're not quite done. I frequently have this case when I am using that nasty kit lens as my reference lens. The trick is to adjust the shutter speed or ISO until you have the closest match and then use this as an offset to the aperture reading on the reference lens. Let's take an example: Suppose that the image from the mystery lens is brighter than the reference lens even when the reference lens is at its widest aperture (lowest f-stop). Suppose that the shutter speed and ISO (for both the mystery lens shot and the reference lens shot) is 1/60 second at ISO 400. Let's assume that your reference lens aperture is f/ 5.6. You notice that when you change the shutter speed of the reference shot to 1/15 second, you get an approximate match in image brightness between the mystery lens image and the reference image. Since each time you change the shutter speed by a factor of two is equivalent to a 1 stop change in aperture, changing from 1/60 to 1/15 is a two stop difference. So your mystery lens is two stops faster than f/ 5.6, which is f/ 2.8. (A one f-stop change is a factor of 1.4. Standard f-stops are 1, 1.4, 2.0, 2.8, 4, 5.6, 8, 11, 16, 22, 32.) By the way, adjusting ISO rather than shutter speed will work just as well. Doubling the ISO is equivalent to a one stop aperture change. Therefore in the example above, increasing the ISO in the reference shot from 400 to 1600 should have produced the same results as decreasing the shutter speed from 1/60 to 1/15 second. If you choose to do this measurement using a flash (which I do not recommend), then adjusting ISO is your only option because adjusting shutter speed will not work. This method gives you an approximate effective focal ratio which takes into account all the optical properties of the lens including light loss due to glass and coating quality. One final note: If you've built a working SLR/DSLR lens with a focal length that measures less than 15 mm or a focal ratio that measures under f/ 0.75 , please let me know as soon as possible. ;-) OK, back to the lab. Originally posted at 6:23PM, 28 April 2010 PST (permalink) johnnyoptic edited this topic ages ago.

..and how do you measure a negative focal lengh ? Originally posted ages ago. (permalink) Thomas Sommer edited this topic ages ago.

A reflection grating is not a mirror. It is an array of reflective grooves in a surface. Light reflected from the bottoms of the grooves is delayed relative to light reflected from the tops of the grooves, just as light transmitted through optically thick portions of a transmission phase grating is delayed relative to light transmitted through the optically thin portions.

The law of reflection (that the angles of incidence and reflection are equal) can be derived directly from Maxwell's equations, or from Fermat's principle. However, reflection gratings completely defy this law, and from light incident at a fixed angle comes a whole diffraction pattern - light reflected at a range of different angles.

Diffractiongrating

nice write up and discussion! I have f0.75 lens(es) just in case... ages ago (permalink)

Instead of taking shots of something that you know the measure of, it's much easier to take shots of a ruler placed parallel to the plane of the sensor. Then the comparison of lenses focal lengths is more "direct". Also shooting the ruler and using the dimensions of the sensor of the camera (or size of film) will give you an easy way to calculate the enlargement of the lens in macro photography. Originally posted ages ago. (permalink) David Sousa-Rodrigues edited this topic ages ago.

genotypewriter: Sorry I didn't see your question until now. Let me try to address them one at a time. First, you are right that the f-stop measurement that I describe relates to light and exposure and that DoF may be somewhat different. I believe that as long as you are using a simple circular stop, the effect of reflections, etc will not throw this off very far. As for the fact that homemade lenses only have much lower contrast making it hard to compare the histogram with the image from a fully corrected lens, the solution is to use a low or no contrast image as your test. For example, just use a plain wall. Loss of contrast is no longer a factor. epatsellis: Thanks for posting the entrance pupil approach to measuring f-stop. Yes, I've used this method many times. Besides the fact that it's a handy method, it's also quite educational to experiment with. ages ago (permalink)

The second method for measuring the f-stop is a nice idea but would it be accurate for lenses with a very bulbous front element? I imagine the paper will need to be touching the surface on the outer most point? ages ago (permalink)

Reflection gratingmeaning

I've done similar shooting graph paper. That is also very helpful to judge distortion. ages ago (permalink)

Thomas Sommer: From an old Sam Brown book: "Make two small holes in a disk of cardboard at any convenient spacing. Place disk over lens. Focus rays [from the sun] to strike target at 2S spacing". The distance from the lens to the target is the focal length of the negative lens. No math needed. I'll post an image from the book. 97 months ago (permalink)

thank you for the inspiration. Using your info and Optical design ebook, I dissasemble all of unused broken scratchy lens, pick the good one, and measure the index and dioptry of each lens element. Using that data, I redesign the lens so I can get the focal length and flange range almost exactly like I want. Sample Image at (about) f2 at (about) f1 99 months ago (permalink)

I agree with Julian (soimless), the best way I know to measure the focal length of a negative lens is to combine it with a positive lens and measure the result. The formula for the resulting focal length from a combination of two lenses (any combination of positive or negative) is: F = (f1 x f2) / (f1 + f2 - d) If the two lenses are right next to each other, you can set d to 0 to simplify things. Assuming f1 is your positive lens of a known focal length and solving this for f2, we get: f2 = (f1 x F) / (f1 - F) Example: Taking a positive lens with a known focal length of 100 mm and placing it right next to a negative lens of unknown focal length produces a combination measured at 150 mm. What is the focal length of the unknown lens? f2 = (100 x 150) / (100 - 150) f2 = -300 Note that the combination of the lenses you are using has to be positive for this to work. A positive lens with a focal length of 100 mm cannot be used to measure the focal length of a negative lens with a focal length of -90 mm, because the combination will be negative and therefore cannot be directly measured. There is one other quick-and-dirty way I use to get the approximate focal length of negative lenses. Rather than taking the time to measure the focal length of the combination of two lenses. I just check to see if the combination results in a positive or negative lens. (By simply looking through the combination to see if it magnifies or reduces.) If the combination is positive, I repeat the process with a weaker positive lens (longer focal length). If the combination is negative I try again with a stronger positive lens (shorter focal length). I repeat this until I find a combination that has the least magnification/reduction. The unknown lens has a focal length of approximately -1 times the focal length of the known lens with which it produces little or no magnification/reduction. ages ago (permalink)