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In 2016 I had an email discussion with the great Pierre Toscani who really clarified the matter of where to make the camera-side measurement for me. The entrance pupil of the lens is the point where the angle of view begins, and unless you have a lot of technical data about the lens formula of the lens in question and are adept at ray-tracing, it is best to find it via experimentation.
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I’ve measured a several lenses this way, each lens multiple times, and the numbers have all come out as I’d expected (after a brief moment of confusion in one case). It’s not my formula, but the equation is simple enough, and certainly makes sense to me. That said, I’m certainly open to the possibility that there’s a mistake or that it’s missing something that would make it more accurate. If it is, and you can explain it to me, I’d be very grateful. Please let me know in the comments below!
Visual: Over the past week, I’ve been looking at a couple of different ways to cross-check my measurements and make sure that what I’m getting makes sense. If you’ve seen my video comparison of the Canon and Tamron lenses and their breathing, you’ve seen a clip from Matt Granger’s video on the subject that shows the effect of breathing on his model while shooting video. It’s a simple, visual comparison but it shows what you’d expect: as the Tamron and Nikon lenses are focused towards the MFD, the subjects get smaller, but on the Canon, the subject gets larger.
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Federal regulations in British Columbia, Northwest Territories, Nunavut, and the Yukon ban cleaning with air due to the risk to workers, although there is some provision for using low noise emitting nozzles with pressures below 10 psi (70 kPa).
After doing this, I went back and measured the focal length of the lens at each of these distances from the subject using the original method that I outlined above. My measured focal lengths were:
First, determine the location of your lens’s entrance pupil (described below), and then measure that distance to the wall (X in the diagram above) I like to use a precise laser measuring tape. My Bosch GLM 50 is accurate to about 1.5mm, but some others are even better. If you’re careful and have some help, a tape measure will also work, though with reduced accuracy.
If that guide didn’t match up with the beginning of the ruler’s scale, then adjust your camera and re-shoot or, if you’re comfortable with the ruler tool in Photoshop, figure out how far away the guide is from the start of the scale, and add or subtract that amount. You can avoid using the ruler tool or making estimates by centering your AF point at the 10cm mark rather than the very end, and then subtracting 100mm (plus or minus adjustments) from your final measurement, but since that adds in another opportunity for errors to creep in to the process, I prefer starting at 0.
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This means that from our two different methods, one in which the camera is a stationary 26 feet from the target and one in which the camera is moved to as close as 5 feet from the target, the numbers support each other pretty nicely.
Once that’s done, center your middle focus-point on the end of the ruler. Since your AF point is most likely a rectangle, the end of the ruler should bisect it, dividing it in half (if your ruler’s scale doesn’t start right at the end of the ruler, then center the first markings on the scale in the center of the AF point instead).
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Landscape photographers often know the entrance pupil as the “Nodal Point” of the lens, and use nodal rails on their camera when shooting panoramas. If you’re shooting a panorama and the pivot point of your camera is directly below the entrance pupil / nodal point, then you’ll avoid parallax problems. Although finding the nodal point is relatively simple, it’s beyond the scope of this article, but there are numerous good tutorials out there already.
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To begin, mount your camera on a tripod near a wall or other vertical surface. Measure from the center of your camera’s sensor to the floor (you can use the vertical center of the lens mount). We’ll call this H. Then, tape something like a metric precision ruler (or metric measuring tape, depending on how wide the lens is) vertically to the wall, with the low end at the exact height of the center of your camera’s sensor from the floor (H). This is just to set up the square angle of a triangle. It’s also important to make sure that the camera is vertically aligned with the ruler.
They’re not a perfect match, of course, but part of that reason is that there was a lot of room for slop in this second measurement; I had to set the focus to 7 feet by looking at the range indicator window on the lens rather than by actually focusing on something, for example. But they’re still pretty close… the worst difference is about 3.75%.
[Update: 10/4/2022] I have updated this article to show a method that is more intuitively easy to understand, and which attempts to measure the angle of view of a lens rather than a focal length directly.
As you can see, I loaded those images into Photoshop, set guides to mark the centers of each light (easier than I expected to get within a few pixels of the center) and then used the ruler tool to measure the distance from center to center. Those distances are marked on the images above.
Other legislation may be applicable in some states, provinces, and countries, so you should always check your local jurisdiction for relevant information. When in doubt, use common sense, and do not use compressed air for cleaning!
Even without the numbers, though, it’s plain to the eye that the lights are getting further apart; the distances involved are not especially subtle. This can be seen simply by looking through the lens and racking the focus. (Note that the CENTERS of the lights are getting further apart, not just the the edges. If I had simply opened the aperture to increase the size of the blur, we’d see results mimicking what you’d expect from zero focus breathing).
I took an under-exposed photo, shot at f/22 (to cut down on bokeh/circle of confusion) with the camera sensor about 26 feet away from the lights, with the lens focused at that distance. The lens, incidentally, was the Canon 70-200 f/2.8L non-IS, since I had read that it behaves similarly to the IS II, but I hadn’t measured it for myself yet. It looked like this:
In the fields below, enter your X measurement for adjacent side, and your Y measurement for opposite side, and press “calculate”. That will give you an the angle we need. We’ll call it A.
Next, load the image into Photoshop. Create a horizontal guide at 50%. That line should match the beginning of the ruler’s scale in the image. From there, it’s simple: look at the top border of the image and read where the ruler leaves the frame. That measurement is the opposite side of the triangle, which we’ll call Y.
Compressed air is powerful and can be dangerous—even deadly—when misused. Air compressors aren’t designed for cleaning, but it’s still common practice to clean the dust and debris from filters, machinery, workshop surfaces, clothes, and so forth using compressed air. To help you understand why you shouldn’t clean with compressed air, we’ll break down the most common risks of cleaning with compressor air.
Some laws in Canada and the United States govern the use of compressed air and, in many cases, it is illegal to clean with compressed air.
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I’ve been involved in an interesting exchange of ideas over the past couple of days with Tony Northrup about the effective focal length of Canon’s 70-200mm f/2.8L IS II lens when it is focused at distances closer than its infinity setting (ie, focus breathing). We’ve been coming up with wildly different numbers (mine were presented in a video last month), and we don’t have many outside sources to check ourselves against… perhaps because making the calculation is not a very straight forward process. So, if you’ve ever had the desire to see how your lenses really measure up or how much they breath, here’s how I do it, with a few of the tools that I use to make it faster.
Once you have found A, you have half of the vertical angle of view of lens, so to get the complete angle of view, just double it. From there, the easiest course it to look up the corresponding focal length based on that angle; there are numerous standardized tables of such things all over the internet, and also tools that will do the exact calculation.
If you remember your geometry, this is pretty easy, but it’s even easier using an online calculator, like this one at EasyCalculation.com.
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I’d also love to hear your results from using other methodology, and your explanations of those methods. It would be great if I could find a testing method that’s easier than this and just as accurate or better.
My favorite of these is Wolfram Alpha, which is accurate and flexible. Click here to see Wolfram Alpha’s “Lens Angle of View” calculation page.
In Canada, cleaning with compressed air is not allowed by law, according to the Canadian Centre for Occupational Health and Safety (CCOHS). Alberta, Saskatchewan, Quebec, Newfoundland, and Prince Edward Island have specific laws that state compressed air must not be used to clean clothes, people, machinery, work benches, and so forth
While incorrect diving procedures are the most common cause of air embolisms, there is also a risk of an embolism when compressed air is misused at high pressures. Although unlikely, high-pressure air can be forced into the bloodstream through cuts and abrasions. It is improbable, but why even take the risk?
I wanted a way to quantify this visual change, and Bob Atkins’ article on focus breathing gave me the idea for a way to do it. He used stars as subjects, but I live in Seattle, so that’s not a practical option (hello cloudy skies). So, instead, I used two small LED lights and did this:
So, if you found an angle of 22 degrees, then the calculation will return 61.73mm as a focal length. Wolfram is an education site, so you can get a full, step-by-step solution if you want one, too.
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Some people have claimed that the Canon 70-200 f/2.8L and IS II do not breath at all. If that were the case, then both of these sets of measurements would have to be off by at least 20% at the 5 foot mark, but hardly at all at the 26 foot end!
Anyone familiar with compressed air used for scuba diving also knows about the potential for air embolisms. Embolisms are a condition in which air bubbles enter the bloodstream and block blood vessels or arteries, with the potential to cause paralysis, induce a coma, or even cause death.
Now, focus the camera and take a photo. If your setup is not completely rigid, take several photos to ensure that the exact center of the image is over the end of the ruler scale.
In the default example, the calculation assumes that we’re measuring using a vertical angle (which we are) and a full frame 35mm sized sensor (36 x 24mm). If you’re using an APS-C camera or another size, enter the vertical size of the sensor instead of 24mm. So, in the computational inputs, enter the angle of view (A) that we found above in the computational input, and press “compute”.
When compressed air enters or contacts your body, you put yourself at risk of significant health complications. Here are a few examples of the dangers of compressed air:
In the United States, Occupational Safety and Health Administration (OSHA) regulates workplace safety. Compressed air use is governed by standard 1910.242.b, which states, “Compressed air shall not be used for cleaning purposes except where reduced to less than 30 psi (206 kPa) and then only with effective chip guarding and personal protective equipment.”
I’m still chewing on some of the details, but instead of using Wolfram Alpha, you can simply paste the formula: 24/(2 * tan(3.22 degrees)) into Google and it’ll give you the answer as well: 213.299798393
Compressed air, especially from commercial air compressors, can exert extremely high forces that turn small particles, nuts, bolts, washers, and other bits into high-velocity projectiles. These objects become shrapnel and can cause severe damage if they hit someone. Even dust and dirt will cause skin abrasions when there is sufficient force behind them—it’s just like sandblasting.
I then focused the lens to about 12 feet away (using the range indicator on the lens) but did not move the camera. The idea here is to get the same effect as Matt Granger’s racking the focus of his lens in his video, but at some distances that I could measure.
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