A few years ago, I realized that I could no longer focus on things up close. I resisted for as long as I could, but it was futile. I had to get reading glasses.
I didn't realize that everybody loses focus range in their eyes as they age. It's called presbyopia. The lens loses flexibility with age. In the graph below, the B line is average, and A and C are the upper and lower standard deviations.
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| By Hans Strasburger - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=39969617 |
For example, reading glasses with +1.50 on the side mean that they magnify 1.5 diopters.
What is a Diopter?
A diopter is 1 divided by the focal distance in meters.Simply put, a set of +1.50 reading glasses will bring the infinity focus point up to 66.7 cm away.
For convenience, here is a list of diopters vs. focal length.
+0.50 = 2 m
+0.75 = 1.33 m
+1.00 = 1 m
+1.25 = 80 cm
+1.50 = 66.7 cm
+1.75 = 57 cm
+2.00 = 50 cm
+2.25 = 44 cm
+2.50 = 40 cm
+2.75 = 36.4 cm
+3.00 = 33.3 cm
+3.25 = 30.8 cm
+3.50 = 28.6 cm
+3.75 = 26.7 cm
+4.00 = 25 cm
+4.25 = 23.5 cm
+4.50 = 22.2 cm
+4.75 = 21.1 cm
+5.00 = 20 cm
So I put on a pair of +1.00 lenses and tried to focus on something one meter away. I soon realized that I couldn't focus out that far. I began to realize that I may be a little nearsighted. So I decided to take some measurements.
Measuring My Focus Range
I tried on all my strengths of reading glasses and measured where it would just start to go out of focus for both near and far distances. With this data, I calculated both my nearsighted correction value and my focal range, or eye accomodation.Here are the measurements I made, in inches.
| Lenses | Near limit, left eye | Near limit, right eye | Far limit, left eye | Far limit, right eye |
| none | 16 | 14 | 52 | 29 |
| 0.50 | 15 | 12 | 40 | 31 |
| 1.00 | 12 | 11 | 28 | 21 |
| 1.25 | 10.5 | 9.5 | 20 | 20 |
| 1.50 | 9.5 | 9.5 | 17 | 14.5 |
| 2.50 | 8 | 7.5 | 13.5 | 12 |
The far focus limit was pretty approximate with no lenses. As lens power increased, it was easier to see where the far distance started to get out of focus.
Next, I converted distance to diopters, first converting inches to meters, then to diopters.
| Lenses | Near limit, left eye (diopters) | Near limit, right eye (diopters) | Far limit, left eye (diopters) | Far limit, right eye (diopters) |
| none | 2.46 | 2.81 | 0.76 | 1.36 |
| 0.50 | 2.62 | 3.28 | 0.98 | 1.27 |
| 1.00 | 3.28 | 3.58 | 1.41 | 1.87 |
| 1.25 | 3.75 | 4.14 | 1.97 | 1.97 |
| 1.50 | 4.14 | 4.14 | 2.32 | 2.72 |
| 2.50 | 4.92 | 5.25 | 2.92 | 3.28 |
With this, I could calculate the focus range in diopters and see how I measured up to the graph of accomodation vs. age.
| Lenses | Left Range (diopters) | Right Range (diopters) |
| none | 1.70 | 1.45 |
| 0.50 | 1.64 | 2.01 |
| 1.00 | 1.87 | 1.70 |
| 1.25 | 1.78 | 2.18 |
| 1.50 | 1.83 | 1.43 |
| 2.50 | 2.00 | 1.97 |
| Average | 1.81 | 1.79 |
With a focus range of 1.8 diopters, it turns out my focus range is amazingly average for my age.
Measuring My Nearsightedness
I can take this one step further. With the far focus range vs. lens value, I can calculate the correction needed for distance vision. I simply subtracted my far limit in diopters from the lens value.| Lenses | Left correction | Right correction |
| 0.50 | -0.48 | -0.77 |
| 1.00 | -0.41 | -0.87 |
| 1.25 | -0.72 | -0.72 |
| 1.50 | -0.82 | -1.22 |
| 2.50 | -0.42 | -0.78 |
| Average | -0.57 | -0.87 |
Armed with this information, I could just order a pair of eye glasses online. But do I have astigmatism too?
Astigmatism
It turns out most people have a bit of astigmatism. That's because the eye lens isn't perfectly shaped. If it magnifies more in one direction than the other, that's astigmatism. It can make objects appear blurry at any distance. If you notice that lines are blurry at certain angles, then you likely have astigmatism. Try printing this focus pattern (link).
I noticed that when I try to focus up close, my astigmatism gets worse (to around 0.50), but if I focus far away, then my astigmatism is not noticeable. That's something to keep in mind for when you check your vision.
First Order Aberrations
A first order aberration is where the focus changes in one direction. If you look at an eye glasses prescription, this would be the number in the cylinder column. It goes along with the number in the angle column. The angle ranges between 0 and 180 degrees because it's symmetrical. If you rotate past 180 degrees, it's like starting over at 0 degrees.Zero degrees is to the left of your eye, and increases in angle as you go clockwise. So if you're the eye doctor looking at the patient, it starts at zero to the right of their eye, and goes counter-clockwise. At least, that's how I understand it. I got that from Wikipedia, so you can read the article on astigmatism and see if you understand it that way too.
If you have astigmatism, you can try rotating your glasses to see if you have the correct angle. I ordered a set of test lenses - just a pair of glasses with only astigmatism correction at -0.25 and -0.5 diopters. I didn't think I had much astigmatism, so that's why I ordered those values. Since I ordered them at 30 degrees, I tied my brain in knots trying to figure out the astigmatism angle. Since the handles got in the way while I rotated them, I looked through them backwards. I could tell which direction looked better, but mentally flipping them around and rotating the angle 30 degrees confused me. I thought I had it down until I came up with different answers.
But I think I got it. If I look backwards through the 30 degree lens and rotate it to 40 degrees clockwise as I look through it, it translates to 10 degrees. Did I confuse you? That's how I felt.
Higher Order Aberrations
If the focus changes in more than one direction, then that's a higher order aberration. If you printed the above focus pattern and see one angle of lines clearly, and the lines at 90 degrees to it are blurry, you probably have only a first order aberration. If you see an X pattern clearly, but the plus angle is blurry, you have a higher order aberration. First order abberations can be corrected. Higher order aberration corrections would be extremely difficult to correct, but may be possible with some creative engineering.Minus vs. Plus Astigmatism Conversion
You can convert negative cylinder to positive cylinder by rotating 90 degrees, and then add back the difference to the spherical number. Every diopter change in cylinder effectually changes a half diopter change in spherical. For example, if you had -1.00 spherical, -1.00 cylinder, at 0 or 180 degrees, then it would be the same as -2.00 spherical, +1.00 cylinder at 90 degrees.My "Prescription"
| SPH | CYL | Angle | |
| OD | -0.75 | -0.25 | 180 |
| OS | -0.25 | -0.25 | 175 |
I'm going to try this without astigmatism correction first. It's nice that you can order online and have the glasses delivered for less than $15. Then once you verified they work for you, you can order more expensive frames and the nice add-ons.
Why didn't I just go to the eye doctor and have him write me a prescription? I wanted to see if I could figure it out. Knowledge is power.
good job!
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