•

# Calculated 'in-focus range', various binoculars

5 replies to this topic

### #1 MartinPond

MartinPond

Skylab

• topic starter
• Posts: 4033
• Joined: 16 Sep 2014

Posted 12 July 2018 - 12:02 PM

Finally...I did it.

The question is:

If I focus a pair of binoculars at something very far away (~infinity),

how close can I look and still see something this is sharp?

In the perfect infinity case, the objective makes an image at the focal length,

the eyepiece's focal plane mates up to that, and you see a virtual image

at infinity (your eyes relaxed)...  So...calculate two relays of the object..

It does depend on your eyes what happens next, but I chose the standard

of 0.5 meters for the closest virtual image I focus clearly without eye strain...

So...my program being written,

here is a table of the effect of power (mostly) on

the 'near-point' of a binoculars' range:

(assume: Fl(obj) = 3.7*Dia , 0.5m closest tolerable final image, focus set at infinity, relaxed eyes)

POWERxObjective      Near-Range Limit (0.5m virtual image distance)

--------------------------    -------------------------

6x30                            17meters

7x35 , 7x50                  23m

8x30                            31m

8x40                            30m

10x50                          48m

15x70                          108m

20x80                          194m

If you want a less claustrophobic, more-exacting standard,

here are  some ranges for a 0.7m virtual image standard:

POWERxObjective      Near-Range Limit (0.7m virtual image distance)

--------------------------    -------------------------

6x30                        24

7x50                        33m

10x50                      86m

20x80                     274m

Other than figuring two imaging sets,

the real tricky part was solving for the desired virtual distance

(of the final image).    Discrete math to the rescue!  I just tried

every distance from 1000meters down to 1 until the virtual image

popped below 0.5 (or 0.7).... voila!

A bit brute-force, but no cumulative errors, and the PC has lots of power to

repeat things.

Edited by MartinPond, 12 July 2018 - 12:07 PM.

### #2 Mark9473

Mark9473

Voyager 1

• Posts: 10982
• Joined: 21 Jul 2005
• Loc: 51°N 4°E

Posted 12 July 2018 - 12:19 PM

I would probably need a table for 50 m closest focus without my glasses... ;-)

A question Martin, we've had some discussions in the past about depth-of-focus and from that I recall that not only the magnification is a factor but also the eye pupil diameter. In broad daylight the eye pupil is typically smaller than most common binocular exit pupil diameters and that creates a larger zone of in-focus image - I hope I'm expressing myself correctly. I felt at the time that my practical experiences were in line with this model.

Any thoughts on this, and how it would fit into your model?

• TOMDEY likes this

### #3 TOMDEY

TOMDEY

Apollo

• Posts: 1406
• Joined: 10 Feb 2014
• Loc: Springwater, NY

Posted 12 July 2018 - 02:04 PM

I would probably need a table for 50 m closest focus without my glasses... ;-)

A question Martin, we've had some discussions in the past about depth-of-focus and from that I recall that not only the magnification is a factor but also the eye pupil diameter. In broad daylight the eye pupil is typically smaller than most common binocular exit pupil diameters and that creates a larger zone of in-focus image - I hope I'm expressing myself correctly. I felt at the time that my practical experiences were in line with this model.

Any thoughts on this, and how it would fit into your model?

Good point! I believe Martin could capture that by adjusting his "closest virtual image I focus clearly without eye strain" in his model.

I DO note that he is making an implicit assumption that his personal range differential is 2.0 diopters. That is, from infinity (not beyond) = 0.0D to half a meter = -2.0D, the delta therefore being two diopters. This is something that the optometrist can accurately measure. That would be more reliable, because nearly all of us have ranges (near point vs far point) that do not have one terminus precisely at infinity. But we (of course) focus the binos to accommodate that, regardless. So, it is the differential diopter range that matters in his assessment. And, yes, that is also pupil dependent.

My case: My personal adaptation dropped to zero, when I got the lenses in my eyes replaced. But, on the +++ side, the implants correct for spherical aberration (present in "natural" eyes), and wavefront-optimized for dilated pupil at true "astronomical infinity." Yes, they now offer that as an option! That gave me 20/12.5 vision, each and both eyes, without eyeglasses, dark-adapted under the stars. Finally see Epsilon Lyrae, naked eye, as two dots with black inbetween.

Anyone out there considering cataract surgeries... ASK the doctors about "astronomical infinity." If you get a blank stare... might want to get another opinion. Otherwise, they will target your focus at some far point that will leave the stars blurry... requiring mild myope glasses. It's Wonderful to be able to see pinpoint stars Without Glasses! Tom

• Rich V. likes this

### #4 MartinPond

MartinPond

Skylab

• topic starter
• Posts: 4033
• Joined: 16 Sep 2014

Posted 12 July 2018 - 02:42 PM

I would probably need a table for 50 m closest focus without my glasses... ;-)

A question Martin, we've had some discussions in the past about depth-of-focus and from that I recall that not only the magnification is a factor but also the eye pupil diameter. In broad daylight the eye pupil is typically smaller than most common binocular exit pupil diameters and that creates a larger zone of in-focus image - I hope I'm expressing myself correctly. I felt at the time that my practical experiences were in line with this model.

Any thoughts on this, and how it would fit into your model?

Right...

I made the standard the 'location of the virtual image' as a precursor to that factor.

Dilating your eyes down would definitely make you tolerate an even closer image.

I have experienced  good performance with even closer (outward) distances than

the above with daytime 6x30s and 7x35s and 7x50s.  How could you drive the modeling

above? Maybe by looking at your reflection and estimating the pupil size, then

illuminating a nearby thing and looking through a little pierced foil hole...

that would let you get much closer to, say, your computer screen in a rough test...

Your "closest squint distance" would then drive the imaging calculation...

So...winging it...

---I make a 2mm hole in paper (simulates bright image, binocs covering all dilations)

---Now I can get ~10in (25cm, or .254meter) from my PC screen... and things are sharp.

I put that into the program as my image distance limit....

a 6x30 can go  inifinity to 8meters  ...wow  <----matches my yard experience

7x50    down to 11 meters ... meh, I can do maybe 13 meters..not bad though.

10x50   23 meters (full sunlight behind you)

20x80   94 meters .............however, at this point you are dimming things..the

exit pupil is 4mm and your eye is opening up....so...it should be higher than this.

It's a little clunky feeding eye pupil in, but it seems to work well, and you can use

a little household feedback (a mirror, the pierced foil/paper pupil)...

I have learned a lot already.... power is a huge factor, but beyond 7x...

...your eye's range comes into play in a handy way in my modeling,

and has a surprisingly big effect....I'll do a few less-tolerant-eye runs a bit later.

Of course, the whole sky is the same focus at night.....this is mostly for day views...

the difference for 250,000 miles and 20 light years is super low.

----------------

I should clarify my 'closest focus':

It is "with my eyes single-corrected for infinity, how close can I then

get to something without blurring"....

-----------------------

I look forward to fiddling more.

-----------------

Edited by MartinPond, 12 July 2018 - 02:47 PM.

### #5 Crusty99

Crusty99

Vostok 1

• Posts: 113
• Joined: 07 May 2018

Posted 12 July 2018 - 07:36 PM

MartinPond...

Thanks for your in-focus range study.

I googled and found the following Cloudy Nights thread (2008) that some may find interesting:

Curvature and Depth of Field

### #6 MartinPond

MartinPond

Skylab

• topic starter
• Posts: 4033
• Joined: 16 Sep 2014

Posted 12 July 2018 - 10:21 PM

Ah, EdZ.... the hardest worker ever on researching and empirically checking things.

To correlate the two things:  he is talking about maintaining focus across the field,

and I am simply working on the range in the center, and assuming a field flat enough

to mostly be subject to "same plane location".....  You might say field curvature would

eat up some of my range..   You could also say that depth of the focus matters

even at long distance.

Narrower fields always have a deeper range, consequently.

I believe some eyepieces can add more depth of focus, but I won't touch that

topic now....It's hard to understand for me now... some super microscope objectives

do that but I can't find a piece I understand on it.

So I modified the simple program so the near-focus can be an argument

So I'll compare a semi-tricky range (10x50) with an eye (corrected if needed) that can

go infinity to 0.5 meters  and one that barely adjusts (say, near-point 5 meters)

D:\all_prog\tcc\tcc-0.9.26-win64-bin\tcc>   binrange 7 50 .5

Dobj: 50.000000 Fobj: 185.000000  pwr: 7.000000  Fep: 26.428571  nearpoint: 0.500000

At range of 23.000000 M , virt. image is at 0.492041 M from eye.

D:\all_prog\tcc\tcc-0.9.26-win64-bin\tcc>binrange 7 50 5

Dobj: 50.000000 Fobj: 185.000000  pwr: 7.000000  Fep: 26.428571  nearpoint: 5.000000

At range of 243.000000 M , virt. image is at 4.981837 M from eye.

Wow....from 23m to 243m!

Bright light and dilation would help a lot,

but that long number still commits you to frequent focusing in nature use.

It also probably means you might need a little nudging for eye variations

over time as well..   I might recommend dark eyecups and little drilled

irises just to be sure you could use the better "error circle", as in a camera..

Edited by MartinPond, 12 July 2018 - 10:25 PM.

## Recent Topics

 Cloudy Nights LLC Cloudy Nights Sponsor: Astronomics