Vision Correction Basics

I never really needed glasses, but knew for as long as I can remember that my right eye didn't focus as well as my left on distant objects. 

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. 

By Hans Strasburger - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=39969617

After I picked out a set of reading glasses, I decided to learn about what the numbers meant. 
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
0.00	-0.76	-1.36
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).  

You can find the angle of your astigmatism by viewing the above focus pattern. (It'll work better if you print out the picture from the link above.) See at what angle the lines towards the center are in focus. Horizontal is zero degrees (or 180). Clockwise from your left is positive. That'll be your negative astigmatism angle. If you add 90 degrees, then that's the positive number (keep reading about the angles). 

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. 

Ford 3.8 V6 Timing Cover Coolant Leak and Why You Should Always Prime the Oil Pump!

This Thunderbird has had a coolant leak ever since I bought it 15 years ago. I smelled coolant then and pretty much ever since. It has always had a coolant leak. No matter how many leaks I fixed, there was always one more. I think I finally found the one that never goes away.

When they made this engine, they made a mistake. Somebody thought it would be a good idea to drill the threads for the timing cover studs into the water jacket. This creates a leakage path through the threads. It also makes the studs rust.

So here's how this repair went wrong.

I got all the bolts and studs out except for the one that wouldn't turn. I put two nuts together and ran my little Makita impact driver on it to loosen it. That didn't work, so I got out the big impact wrench. I figured that'll do it. It quickly broke the stud off, flush with the timing cover.

I figured I could pry the timing cover off. I got a big crow bar and pried too hard and broke the timing cover, but exposed more of the stud, shown below.

This gave me the opportunity to waste a week soaking it with penetrating oil while attempting to unscrew it. Every try to turn the stud using tightened double nuts was a failure.

I started pulling on it. Then I wedged screw drivers in and pushed on the opposite side. Then I got out the 12 pound sledge hammer and started whacking the opposite side, trying to pry it off. My neighbor Brent came over, kind of concerned, and asked what I was doing. 

I knew he was right when he suggested just getting out the air hammer and chiseling down the timing cover to expose the stud. This thing's coming out in pieces!

After this, I was able to pry it off. 

Re-Assembly

Here's my solution to stop the eternal coolant leak. I put RTV on the threads of the new stud and installed it. I let it cure before installing the new timing cover. (It's the only stud installed in this picture.)

When aligning the camshaft position sensor, you need to set the crankshaft at 26 degrees after TDC. That's right at the edge of this slot that I'm pointing to with a ball point pen.  

My original timing cover had a much better pointer for reading timing than my new cover has. Compare the pointer in this picture to the one in the next picture.

The replacement cover just has an arrow on the surface. I'm feeling short-changed. 

I aligned the crankshaft to 26 degrees after TDC by lining up the slot with the timing mark. I installed and aligned the camshaft position sensor so that the half circle was towards the engine and the edges of the half circle were aligned in the middle of the sensor. Sorry I didn't get a picture of that. 

Why You Should ALWAYS Prime a New Oil Pump

After re-assembling everything, I started up the engine. After every oil change, there's that pause before you get oil pressure. This time, the pause didn't stop. I kept waiting for the oil pressure to build and nothing. The gauge was at zero. I took off the oil filter and started the engine. Nothing came out. 

I removed the oil pump and everything looked ok except there was no oil in it. I learned something there. Without oil in the pump, it will not create sufficient vacuum to draw the oil up from the oil pan. It will just spin and the air will blow past the vanes. You need oil to fill the gaps and create a seal. 

I figured grease would work even better, so I put grease in the oil pump and spun it to make sure everything in there was coated. 

After re-installing the oil pump, I started the engine. This time I heard a ticking noise for a second

until it got oil pressure.

This reminded me of my idea of a bypass electric oil pump. It would be nice to have an electric oil pump run to build up oil pressure before the starter is allowed to turn. 

Was everything good after I got it all back together? Of course not. The water pump went bad and I had to replace it too.