CA, Southern California, 20070930
Madison Heights, horse mushroom.
Agaricus californicus []
Same spot: NW corner Fillmore and Marengo. This place has been producing fairly regularly for months now. Just wanted to study another one in detail after found new info on web.
| GEN | med mushroom, scattered to clustered in lawn |
| ST | short (cap gen sits on grass) 60x10-15mm, solid, whitish, firm, not staining when cut, small skirt-like ring |
| CAP | 80mm, brownish and shiny to white w flat thin brown scales, appressed fibrillose (esp obvious in age), darker in full sun, K+amber after about 30-60sec, opening quickly to convex (broadly umbo) to plane |
| FLESH | white, firm, K+y in about 15-30sec |
| GILL | white as button to brown, free, close |
| SPORE | print choc brown, ellip, smooth, brown, one bubble, 4.9-6.3x3.5-4.2um |
I did a side-by-side comparison of measuring dry spores at 400x to wet spores at 1000x to see how much error that causes. (Measuring dry at 400x is much easier no coverslips or nasty oil involved, and the darned spores don't have to be coaxed into staying still!) To get a statistically significant defensible, I measured about 20 spores both wet and dry to estimate the full distribution:
dry wet
mean 4.74 3.67 5.60 4.15
sigma 0.41 0.30 0.30 0.26
median 4.87 3.69 5.57 4.20
min 4.03 3.19 5.05 3.73
max 5.54 4.36 6.23 4.65
Difference in means:
4.74 vs 5.60 = 0.86 +/- 0.51
3.67 vs 4.15 = 0.48 +/- 0.40
Indeed, wet spores are significantly larger, as I suspected, in this case about 15% +/- 8% larger. It would be interesting to know how much of a difference this makes for various other families. For example, some spores start out sort of goopy and sticky, while others look deflated and almost raisin-like when dry.
Calibration of Microscope Objectives
Okay, I'm tired of not having my objectives calibrated. It seems with a bit of care, I don't need an expensive calibration slide to do it. I've taken a bit of newsprint with dots spaced about 4 per mm, taken photos under 40x and 100x, as well as at 10x next to a ruler. Measuring the distance between ruler marks and fitting a line to it gives me the calibration for the 10x shot (any non-linearity should show up here, as well). Now I can measure the density of dots accurately, and thereby calibrate the 40x and 100x objectives. Then I need to find some spores (from some Pertusaria for example) that are around 80-120um long big enough to measure at 100x, 400x, and still fit in the field of view at 1000x. Admittedly, I'm compounding 3 errors to reach 1000x, but if I can keep the uncertainty down on the first (easy) measurements, it shouldn't be too bad.
First, calibrate 10x objective and newsprint dots using ruler:
marks pixels dots pixels
1 141.0 36 1157.6
2 279.4 32 1027.8
3 411.4 28 897.8
4 546.7 24 767.2
5 684.9 20 639.5
6 816.9 16 511.8
7 948.9 12 383.3
8 1087.3 8 256.3
9 1216.3 4 129.3
10 1351.5
11 1483.6 4 126.5
12 1615.7 8 253.6
13 1753.6 12 382.2
14 1885.7 16 511.5
15 2021.0 20 639.9
16 2155.9 24 770.0
17 2291.0 28 900.6
18 2423.3 32 1031.3
19 2564.2 36 1165.5
20 2699.3
4 130.7
8 261.8
12 390.5
16 521.8
20 654.4
24 784.4
4 129.3
8 257.1
12 384.9
16 511.8
20 639.7
24 769.5
28 897.2
32 1027.8
36 1156.8
The ruler gives 134.24 +/- 0.11 pix/mm, R-square is 1.00(!!) No noticeable non-linearity (plotted estimation errors).
Nesprint gives 32.185 +/- 0.076 pix/dot, R-square again 1.00. There is definitely some non-linearity here. Doing an ANOVA on estimation errors divided by num_dots shows that set number three above is off by a signficant amount (F-stat = 25). (The other three are the same, giving an F-stat of 0.78.) I'm concerned about this. Here's what that distorted third set does to the slope:
just set 3 32.697 0.062 1.00
w/o set 3 32.224 0.045 1.00
total 32.185 0.076 1.00
Not sure why the slope of the total is less than either part. Must have something to do with intercept, which I can't force to zero as I should. I'll add that feature to my stats program later. In the meantime, I'll average the two parts: 32.461 +/- 0.077 pix/dot.
Combining the two results, I get 4.135 +/- 0.010 dot/mm. (To approximate the uncertainty, I'm just taking the root sum of the squared uncertainties of the parts as fractions that is sqrt(0.11/134^2 + 0.076/32^2) * 4.1. This is good if the uncertainties are small relative to the means. In this case they are 0.08%, 0.2% and 0.25%, for pix/mm, pix/dot and dot/mm, respectively.)
Now, the 40x objective:
dots pixels marks pixels
14 1947.8 100 1488.0
11 1533.0 90 1338.0
12 1648.3 80 1188.0
8 1095.9 70 1040.0
7 951.7 60 894.0
10 1387.9 50 748.0
12 1659.6 40 594.0
8 1102.2 30 446.0
6 832.0 20 298.0
7 954.4 10 162.0
4.135 +/- 0.010 dot/mm
140.4 +/- 1.1 pix/dot R^2 = 1.0
14.793 +/- 0.044 pix/mark R^2 = 1.0
-------------------------
25.48 +/- 0.22 um/mark
(reads too small by 1.9 +/- 0.9 percent)
Now, the 100x objective:
dots pixels marks pixels
4 1419.2 100 1491.4
3 1061.2 90 1335.4
2 731.5 80 1188.4
3 1091.0 70 1038.4
3 1075.6 60 888.3
5 1785.3 50 747.2
6 2146.8 40 594.1
5 1771.1 30 450.0
4 1414.9 20 297.1
2 709.5 10 129.0
4 1418.1
3 1060.9
5 1759.0
4 1402.5
2 692.7
4.135 +/- 0.010 dot/mm
354.7 +/- 3.0 pix/dot R^2 = 1.00
14.894 +/- 0.043 pix/mark R^2 = 1.00
--------------------------
10.155 +/- 0.094 um/mark
(reads too small by 1.5 +/- 0.9 percent)
Now, the 400x objective, using crappy photo:
dots pixels marks pixels
1.414 2065.3 100 1490.6
1.414 2160.5 90 1340.1
1 1453.3 80 1192.4
1 1458.7 70 1045.1
1 1489.9 60 897.4
1 1503.7 50 746.9
40 593.5
30 446.0
20 295.2
10 144.8
4.135 +/- 0.010 dot/mm
1487 +/- 16 pix/dot R^2 = 1.00
14.948 +/- 0.023 pix/mark R^2 = 1.00
----------------------------
2.431 +/- 0.027 um/mark
(reads too large by 2.8 +/- 1.1 percent)
Alternatively, I can calibrate the 100x, 400x and 1000x relative to each other. In this case I used a bunch of Pluteus cervinus spores I happened to have lying about. I fixed the coverslip really well to keep the pattern exactly the same between the three photos. If I match spore for spore, I should be able to compare the three nicely.
First, I still need to do the reticle on the 1000x photo (I've already done it for the other two). Oops, actually if they're all independent of the objective, I can ignore this conversion factor altogether. But here it is anyway.
marks pixels
100 1488.2
90 1337.1
80 1186.4
70 1038.3
60 890.2
50 742.4
40 594.7
30 443.6
20 292.9
10 144.8
14.905 +/- 0.016 pix/mark R^2 = 1.00
As these should be independent of the objective, I will just average them:
100x 14.894 +/- 0.043 pix/mark
400x 14.948 +/- 0.023 pix/mark
1000x 14.905 +/- 0.016 pix/mark
--------------------------------
mean 14.916 +/- 0.017 pix/mark
Now I'll make a series of identical measurements in each objective:
A B C D E F G
100x 400x 1000x 100x 400x 400x 1000x
170.2 679.3 1783.1 380.1 1535.4 811.0 2125.6
160.0 642.1 1678.6 362.6 1462.2 936.8 2463.8
124.9 502.1 1316.6 261.8 1046.8 892.9 2360.2
116.5 468.8 1223.5 229.6 913.6 906.1 2398.0
182.4 729.0 1901.7 155.4 628.2 326.4 864.8
103.0 412.3 1073.7 352.6 1412.1 226.3 613.6
60.3 240.4 623.9 191.5 760.9 446.6 1167.4
157.8 634.2 1668.6 180.9 724.5 238.5 627.9
139.3 561.9 1474.0 148.9 587.8 216.1 573.6
179.3 717.5 1887.0 181.0 723.1 216.0 567.0
153.1 610.6 580.1 1506.0
187.0 748.8 488.7 1278.3
128.5 513.0 614.6 1590.6
211.9 846.2 682.0 1788.1
148.3 597.7 375.9 966.5
400x / 100x = 4.009 +/- 0.015 (B/A)
1000x / 100x = 10.289 +/- 0.073 (C/A)
1000x / 400x = 2.616 +/- 0.012 (C/B)
400x / 100x = 4.002 +/- 0.026 (E/D)
1000x / 400x = 2.628 +/- 0.033 (G/F)
400x / 100x = 4.006 +/- 0.015
1000x / 400x = 2.622 +/- 0.018
1000x / 100x = 10.397 +/- 0.055
This gives me two separate calibrations for the 400x objective, the one above based on the crappy photo, and another using the calibration for 100x divided by the ratio measured above:
2.431 +/- 0.027 um/mark (crappy photo)
2.535 +/- 0.025 um/mark (100x / ratio)
-----------------------
2.483 +/- 0.025 um/mark
(The two are not statistically independent, so I'm not willing to reduce the uncertainty to 0.018 as would normally be done.)
Summary:
Objective Mark Equals Adjustment
40x 25.48 +/- 0.22 um/mark +1.9% +/- 0.9%
100x 10.155 +/- 0.094 um/mark +1.5% +/- 0.9%
400x 2.483 +/- 0.025 um/mark -0.7% +/- 1.0%
1000x 0.977 +/- 0.010 um/mark -2.3% +/- 1.0%
I'm sure I could get a far better calibration with proper equipment, but this at least puts some reasonable bounds on it. In particular, it proves that my 1000x objective is not 10% off as I long supposed it to be. Whaddaya know. And frankly, if a 2.5% error in measurement makes a difference in an identification, it raises all sorts of questions about the validity of the species involved! So I will most likely continue to ignore calibration unless I'm trying to be really pretentious.