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HoloMath help?

james_ashleyjames_ashley ✭✭✭✭
edited March 2016 in Questions And Answers

Alex Kipman's TED talk was amazing and at the end he said something really important about the HoloLens FOV being the wrong thing to concentrate on. Instead we should be concerned with Holographic Density. I've been having trouble figuring out the details of this, though.

Can you all help me with my holomath?

This is something my friend Andras Velvart and I worked on a while back.

Here are the givens:

The HL pixel resolution is 1260 * 720 per eye, which is approximately HD (1280 x 720 with a 16:9 aspect ratio).

There are 2500 light points per radian.

The HL light engines generate 2,800,000 light points.

**Here are some definitions: **

Holographic Density = the number of light points in a radian = one radiant = 2500.
Holographic Resolution = Total number of light points emitted = 2.8 million.

That all comes from the documentation and some follow-up on the forums.

The holomath:

If there are 2500 light points in a radian, then there are 6,250,000 light points in a square radian (rad^2). Square radian isn’t a standard measurement, but it is recognized in some places.

As you can see this is bigger than the current Holo resolution, so the resolution is less than a square radian.

There are approximately 57.3 degrees in a radian, which means there are 3,283.3 square degrees in a square radian (57.3 ^2).

If we divide 6.25 million, the number of light points / rad^2, by 3,283.3 we get the number of light points in a deg^2: 1903.57.

There are 1903.57 light points per square degree.

(As an aside, that's 0.76 radiants per deg^2.)

So what's the HL resolution in square degrees?

We can now get that by dividing the total number of light points (2.8 million) by the number of light points per square degree. This gives us 1470.76 total deg^2.

How does this translate back to pixel resolution? Badly, actually, which indicates my math has gone astray along the way.

For simplification, we’re going to say that the pixel resolution has a 16:9 aspect ratio.

A rectangle with sides that are 16 degrees by 9 degrees gives us an area of 144 sq degrees.

(x^2) * 16 * 9 = 1470.76.

(10.21) * 16 * 9 = 1470.76.

x = 3.2.

The angular size of this screen, then would be 51.2 degrees by 28.8 degrees. The length of the diagonal on this rectangle would be 58 degrees.

This, however, is higher than the observed size of the HL visible display -- and also higher than what current waveguide tech should be able to provide -- so I did something wrong along the way.

Can anyone help?

James Ashley
VS 2017 v5.3.3, Unity 2017.3.0f3, MRTK 2017.1.2, W10 17063
Microsoft MVP, Freelance HoloLens/MR Developer
www.imaginativeuniversal.com

Best Answer

Answers

  • Dave_WDave_W
    edited March 2016
    @james_ashley I don't know if this makes a difference but the hardware spec lists the holographic resolution at 2.3 mill light points. I can't double check the math right now though.

    https://dev.windows.com/en-us/holographic/hardware_details

    Edit: Are you estimating the "observed size of the HL visible display"? Or is this posted somewhere?
  • james_ashleyjames_ashley ✭✭✭✭

    @Dave_W, I don't know where I got the 2.8 million. You're right! Thanks.

    By "observed size" I mean guestimates various people have made by trying to measure known lengths through the hololens at demos -- for instance putting your thumbs together and viewing it at full arms length, then later checking what the angle is from pinky tip to pinky tip.

    Also, the 2500 light points per radian appears to be a minimum density in the hardware explanation. If that number can be higher, does that mean the 2.3 mill resolution can go higher, too?

    2.3 million returns 46.4 degrees by 26.1 degrees, and 1208.26 square degrees.

    James Ashley
    VS 2017 v5.3.3, Unity 2017.3.0f3, MRTK 2017.1.2, W10 17063
    Microsoft MVP, Freelance HoloLens/MR Developer
    www.imaginativeuniversal.com

  • @james_ashley I'd guess that the 2.3M resolution is also a rough number, not exact. Hopefully Microsoft releases a more detailed specifications list at some point.

  • Keep in mind the brightness setting impacts this iirc. That's what I concluded after reading the design docs at least!

  • james_ashleyjames_ashley ✭✭✭✭

    @wintermoot,

    So turning up the brightness provides a holographic resolution above 2.3M points of light? Is this what you mean?

    James Ashley
    VS 2017 v5.3.3, Unity 2017.3.0f3, MRTK 2017.1.2, W10 17063
    Microsoft MVP, Freelance HoloLens/MR Developer
    www.imaginativeuniversal.com

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