did you LiDAR undergo a refraction calculation?

[Martin Isenburg]

Hello,

This is a follow-up to the discussion on improving the hard-to-implement-correctly wording of the full waveform part of the LAS 1.3/1.4 specifications:

http://groups.google.com/d/topic/lasroom/g4VsXH3CRZo/discussion

http://groups.google.com/d/topic/lastools/g4VsXH3CRZo/discussion

I am looking for multi-return LiDAR data in LAS format where you are sure that a proper refraction of the laser pulse either by the atmosphere or by the water surface was considered in the calculation of the returns. I need overheanging vegetation in the case of water to get sufficiently many returns.

In order to check this I need at least three returns R1, R2, R3 from one pulse. Then I can simply check whether the two vectors V1->V2 and V2->V3 are colinear or not. Of course they will not be exactly colinear because the LiDAR returns are quantized onto a grid with (typically) centimeter resolution. So I have to disregard any non-colinearity that has do to with the quantization by allowing a "wiggle" of one unit of resolution (or so) in all directions. 

I wrote a little tool that does this analysis based on the attached formulas. On (the few) topographic data sets that I have tested so far I do not seen any concrete evidence for a refraction calculation.

Here a small output for a heavily vegetated area (= many multi-returns) when allowing an error of 0.75 (and 0.5) resolution units (units are 0.01 m). The first interval [0,0.01) is the amount the angle is bigger than the error in degrees. The second number 5.45705 is the average scan angle of all (17) cases that fell into the bin [0,0.01). For details on the forumlas I use see the attached illustration.

D:\LAStools\bin>laspulse -i sample_sorted.laz -histo angle_bigger_error 0.01  -error 0.75

angle bigger than error [degrees] histogram of averages with bin size 0.01

  bin [0,0.01) average has 5.45705 (of 17)

  bin [0.01,0.02) average has 7.88778 (of 12)

  bin [0.02,0.03) average has 7.82674 (of 7)

  bin [0.03,0.04) average has 8.89233 (of 4)

  bin [0.04,0.05) average has 4.20227 (of 3)

  bin [0.05,0.06) average has 4.68921 (of 2)

  bin [0.06,0.07) average has 5.67395 (of 1)

  bin [0.07,0.08) average has 6.4139 (of 1)

  bin [0.08,0.09) average has 25.9835 (of 1)

  average angle bigger than error [degrees] 0.0217497

angle_was_bigger: 48

error_was_bigger: 7433 

D:\LAStools\bin>laspulse -i sample_sorted.laz -histo angle_bigger_error 0.01  -error 0.5

angle bigger than error [degrees] histogram of averages with bin size 0.01

  bin [0,0.01) has average 6.60165 (of 237)

  bin [0.01,0.02) has average 6.74692 (of 199)

  bin [0.02,0.03) has average 6.927 (of 145)

  bin [0.03,0.04) has average 5.60133 (of 152)

  bin [0.04,0.05) has average 6.07346 (of 101)

  bin [0.05,0.06) has average 6.70201 (of 102)

  bin [0.06,0.07) has average 5.69322 (of 81)

  bin [0.07,0.08) average has 6.6355 (of 62)

  bin [0.08,0.09) average has 6.18434 (of 46)

  bin [0.09,0.1) average has 6.44559 (of 43)

  bin [0.1,0.11) average has 6.15146 (of 38)

  bin [0.11,0.12) average has 6.25207 (of 31)

  bin [0.12,0.13) average has 5.84629 (of 24)

  bin [0.13,0.14) average has 7.11392 (of 17)

  bin [0.14,0.15) average has 8.26239 (of 15)

  bin [0.15,0.16) average has 8.26413 (of 12)

  bin [0.16,0.17) average has 4.11885 (of 6)

  bin [0.17,0.18) average has 4.65816 (of 4)

  bin [0.18,0.19) average has 4.53317 (of 8)

  bin [0.19,0.2) average has 5.2924 (of 5)

  bin [0.2,0.21) average has 4.75854 (of 2)

  bin [0.21,0.22) average has 10.2464 (of 4)

  bin [0.22,0.23) average has 5.86678 (of 2)

  bin [0.23,0.24) average has 4.29368 (of 4)

  bin [0.24,0.25) average has 5.17868 (of 3)

  bin [0.25,0.26) average has 5.04914 (of 2)

  bin [0.26,0.27) average has 4.97388 (of 1)

  bin [0.27,0.28) average has 5.3555 (of 1)

  bin [0.31,0.32) average has 6.49198 (of 1)

  bin [0.33,0.34) average has 4.34348 (of 2)

  bin [0.34,0.35) average has 4.30976 (of 1)

  bin [0.36,0.37) average has 4.04272 (of 1)

  bin [0.4,0.41) average has 4.22064 (of 1)

  bin [0.61,0.62) average has 22.5806 (of 1)

  bin [0.73,0.74) average has 5.65066 (of 1)

  average angle bigger than error [degrees] 0.0516696

angle_was_bigger: 1355

error_was_bigger: 6126

Does anybody have data that is *definitely* refraction corrected? I want to see how this looks different in the outputs 

Regards,

Martin @rapidlasso

[Kirk Waters - NOAA Federal]

Martin,

We definitely have a number of data sets with refraction as part of the processing steps. I'd be surprised and disappointed if any of our topobathy data sets didn't. The harder part to know is if there are pulses with multiple returns above water plus at least one below. All our topobathy datasets can be listed through http://coast.noaa.gov/dataregistry/search/collection/info/jalbtcx (note, if your browser flips that to https you may have to enable scripts coming from http for the page to work. I know I have to). 

I may be able to narrow the search down a bit by looking for something with a return number of 3 or more and classed as bathy (any of 11, 26, or 29 for our holdings). I'll see if I can rig up that search.

Regards,

Kirk

--

Kirk Waters, PhD                     | NOAA Office for Coastal Management

Applied Sciences Program      | 2234 South Hobson Ave
843-740-1227                          | Charleston, SC 29405    

coast.noaa.gov/digitalcoast

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