Visual acuity vs. Refractive state

[johnlink]

Here is a link to a paper that reported the results of experiments to estimate the relationship between visual acuity and refractive state. http://journals.lww.com/optvissci/Abstract/1990/01000/Effects_of_Dioptric_Blur_on_Snellen_and_Grating.2.aspx

I determined that Figure 1 in the paper can be approximately summarized by the following equations:

     1) A = 20                when D=0

     2) A = -48 - 88*D    when D is less than or equal to -1

where A is the denominator of the visual-acuity fraction (e.g., in 20/40, A=40)
and D is the refractive state measured in diopters (a negative D indicates myopia).


Equation 2 generates the following:

     D=-1 -> 20/40

     D=-2 -> 20/128

     D=-3 -> 20/216

     D=-4 -> 20/304


Let's solve equation 2 for D in terms of A:

     3) D = -(A + 48)/88    when A is greater than or equal to 40


Equation 3 generates the following:

     20/40 -> D=-1.0

     20/60 -> D=-1.2

     20/80 -> D=-1.5

     20/100 -> D=-1.7

     20/200 -> D=-2.8

     20/300 -> D=-4.0

We would expect someone with the visual acuity to the left of the arrow to need a lens with the diopters listed to the right of the arrow in order to clear the 20/20 line. For example, we would expect someone with 20/80 visual acuity to need a lens of -1.5 diopters in order to clear the 20/20 line.

[johnlink]

I would agree that if you read the 20/40 line, and you find that a -3/4 diopter "just clears" the 20/20 line, then your refractive STATE (always self-measured) is -3/4 diopters.

Based on the statement I quoted above I now realize that I had the sign of the definition of refractive state reversed. In the situation you described above I would have said that the refractive state was +3/4 diopters rather than -3/4 diopters. I have therefore edited my initial post in this thread to correct my mistake.

[johnlink]

I have made a slight change in Equation 2 above, so that it now appears as follows:

     2) A = -48 - 88*D    when D is less than or equal to -1

The revised Equation 2 fits Figure 1 in the paper cited above as well as the original Equation 2 did but is slightly easier to use (because 88 is divisible by 4 but 87 is not).

I have also revised Equation 3 accordingly so that it now appears thus:

     3) D = -(A + 48)/88 when A is greater than or equal to 40

Equation 1 is unchanged:

     1) A = 20                when D=0

We can summarize these equations by saying that with no myopia (D=0) there is 20/20 acuity. With one diopter of myopia (D=-1) there is 20/40 acuity, and for each additional diopter of myopia there is an increase of 88 in the denominator of the visual-acuity fraction. Thus the first diopter of myopia increases the denominator of the visual-acuity fraction by 20, taking us from 20/20 to 20/40, while each additional quarter diopter of myopia increases the denominator of the visual-acuity fraction by 22).

Note that Equations 1-3 do not say how A and D are related when D is between 0 and -1 (and visual acuity is between 20/20 and 20/40). Although the paper cited above made no observations in that range, let's assume there is a linear relationship:

     1*) A = 20 - 20*D    when D is less than 0 and greater than -1  


Equation 1* generates the following:

     D=-.25 -> 20/25

     D=-.50 -> 20/30

     D=-.75 -> 20/35


Here are all of the equations displayed together:

     1) A = 20                  when D=0

     1*) A = 20 - 20*D      when D is less than 0 and greater than -1

     2) A = -48 - 88*D       when D is less than or equal to -1

     3) D = -(A + 48)/88    when A is greater than or equal to 40

[johnlink]

To extend your equation - please project a person's visual acuity when their refractive STATE is a normal +1.0 diopters.

In the paper cited above there were no observations made to provide the basis to do what you request.
 
Why do you say that +1.0 is normal?

[johnlink]

Why do you suggest that a refractive STATE (self-measured) is not normal?

If you meant to write "Why do you suggest that a refractive STATE (self-measured) of +1.0 is not normal?", I made no such suggestion.

But it seems to me that you asserted that a +1.0 refractive state IS normal ("please project a person's visual acuity when their refractive STATE is a normal +1.0 diopters."). Please explain why.

[johnlink]

Hi John,

Subject: What is the refractive STATE of the totally normal eye.

Regarding: Range of refractive states of the primate eye.

They range from zero diopters to about +3.0 diopters - and are normal.

The average for the normal eye is about +1.0 diopters.

That is why I suggest that a refractive STATE of +1.0 diopters and 20/20, (measured, objectively,  with trial-lens and Snellen)  is normal.

I believe you agreed that the definition of refractive state is the power of the lens needed to just clear 20/20. If one has 20/20 vision without a lens then the refractive state is 0.0, contradicting your statement that "a refractive STATE of +1.0 diopters and 20/20 is normal". That is, according to the definition of refractive state one with 20/20 vision has a refractive state of 0. Maybe the normal eye is better than 20/20 (e.g., whatever it would be with a refractive state of +1.0), but in any case, according to the definition of refractive state one with 20/20 vision has a refractive state of 0.

Are we agreed that myopia is indicated by a negative refractive state? I'm just asking about the convention regarding the sign of the number.

[Steven]

johnlink, the analysis you made is wrong.

Perfect eye vision for a human eye is maximum 20/8 proven by engineers !

20/8 means -0.4 diopters and 2.5 meters of perfect sight. You can't go lower than -0.4 diopters.

20/20 is -1 diopter and 1 meter of perfect sight.

20/20 is not 0 diopters because if i have 20/10 i have 2 times better vision than you.

******

If you think you have 0 diopters with 20/20 then with 20/8 how many diopters do you have ?

[johnlink]

johnlink, the analysis you made is wrong.

Perfect eye vision for a human eye is maximum 20/8 proven by engineers !

20/8 means -0.4 diopters and 2.5 meters of perfect sight. You can't go lower than -0.4 diopters.

20/20 is -1 diopter and 1 meter of perfect sight.

20/20 is not 0 diopters because if i have 20/10 i have 2 times better vision than you.

******

If you think you have 0 diopters with 20/20 then with 20/8 how many diopters do you have ?

Steven, I will respond to your post in great detail later today or tomorrow.