Confocal Microscopy
Confocal Microscopy enables imaging of thin optical section in optically thick specimens (living biological tissue).
Many students (such as pictured above at Confocal Day, 6-24-09) are becoming interested in confocal as an interesting and powerful tool.
The two matlab codes below calculate the optical power of the confocal optical signal falling on a detector as a function of the power of the laser used and the molar concentration of the fluorescent chemical species in the focal region.
Matlab instructions:
- Download the two Matlab files
- Check out the comments in the code
- Adapt the code for your experimental conditions
- Run the program
Source code in Matlab:
Master Code
clear all
close all
%The molar extinction coefficient of Eosin Y dissolved in basic ethanol
%based on the absorbance measurements made by Junzhong Li on 12/11/97 using
%a Cary 3 [H. Du, R. A. Fuh, J. Li, A. Corkan, J. S. Lindsey,
%"PhotochemCAD: A computer-aided design and research tool in photochemistry
%," Photochemistry and Photobiology, 68, 141-142, 1998]. The absorbance data
%was normalized to have an extinction coefficient of 112000 at 524.8 nm
%[P. G. Seybold, M. Gouterman, and J. Callis, "Calorimetric, photometric
%and lifetime determinations of fluorescence yields of fluorescein dyes,"
%Photochem. Photobiol., 9, 229-242, 1969].
%To convert this data to absorbance A=-log10(T), multiply by the molar
%concentration and the pathlength in centimeters. To convert this data to
%absorption coefficient in (cm-1), multiply by the molar concentration and 2.303.
EoData % Loads Eosin data data[nm extcoef]
figure(1)
plot(data(:,1),data(:,2),'k-')
xlabel('wavelength [nm]')
ylabel('Molar extinction coefficient [cm^-1/M]')
% Optical sectioning
title('pick wavelength (click, hit enter)')
samp = ginput;
lambda = samp(1)*1e-9; % [m] wavelength
NA = 0.9; % [-]
dZ = 2*0.63*1.34*lambda/NA^2; % [um]
QY = 0.5; % [-] quantum yield of fluorescence
data(:,2) = data(:,2)*100; % Ext. Coef. [cm-1/M] --> [m-1/M]
n = 100; % [-] sample points
Pmax = 50e-3; % [W] laser power
dP = Pmax/n; % [W] laser power
cMAX = 1; % [mM]
dc = cMAX/n; % [mM]
T_optics = 0.5; % [-] transmission to the sample
T_tissue = exp(-60*0.0100); % [-] = exp(-[cm-1][cm])
T = T_optics*T_tissue; % [-] Total Transmission
ix = 0;
for Plas = dP:dP:Pmax
ix = ix +1;
Po(ix) = Plas*T;
iy = 0;
for cMM = dc:dc:cMAX
iy = iy +1;
c(iy) = cMM / 1000; % [mM-1] --> [M-1]
mua(iy) = c(iy)*samp(2); % [m-1] = [M-1]*[m-1/M]
Pabs = Po(ix)*(1-exp(-mua(iy)*dZ)); % [W] absorbed in confocal vol
Pemit = Pabs*QY; % [W] emitted from confocal vol
Pdet(ix,iy) = Pemit*T ;% [W] detected
end
end
figure(1)
surf(Po/T,c*1000,Pdet)
xlabel('laser power [W]')
ylabel('concentration [mM]')
zlabel('detected signal [W]')
% break
Lp=input('laser power (in Watts)?');
Ceo=input('concentration (mM)');
Ceo=Ceo/1000;
P10=Lp*T;
mua=Ceo*samp(2);
P1abs=P10*(1-exp(-mua*dZ));
P1emit=P1abs*QY;
P1det=P1emit*T;
figure(1);
title(sprintf('The light at detector=%0.3e(W)',P1det),'fontsize',14)
Eosin Data
data = [
219.75 32895
220.00 31973
220.25 32689
220.50 31935
220.75 31286
221.00 30902
221.25 31456
221.50 31019
221.75 31351
222.00 29886
222.25 29802
222.50 30350
222.75 30233
223.00 29301
223.25 29811
223.50 28066
223.75 29315
224.00 28876
224.25 28053
224.50 28296
224.75 28752
225.00 27995
225.25 28393
225.50 28243
225.75 28182
226.00 27857
226.25 27796
226.50 26833
226.75 27795
227.00 27159
227.25 27040
227.50 27707
227.75 26195
228.00 27684
228.25 27338
228.50 27681
228.75 26818
229.00 25920
229.25 26701
229.50 26389
229.75 26460
230.00 27359
230.25 27089
230.50 26482
230.75 26348
231.00 26392
231.25 26574
231.50 26352
231.75 26049
232.00 26149
232.25 26884
232.50 26749
232.75 27129
233.00 26155
233.25 26877
233.50 26285
233.75 26522
234.00 26406
234.25 26570
234.50 27457
234.75 26276
235.00 27505
235.25 26902
235.50 27004
235.75 27786
236.00 26780
236.25 27154
236.50 27074
236.75 26286
237.00 27552
237.25 27188
237.50 27719
237.75 27404
238.00 26989
238.25 27754
238.50 27703
238.75 28055
239.00 27952
239.25 27360
239.50 27659
239.75 28481
240.00 27878
240.25 28418
240.50 28517
240.75 27913
241.00 28231
241.25 27960
241.50 28570
241.75 28630
242.00 29269
242.25 29095
242.50 28778
242.75 28249
243.00 28271
243.25 28735
243.50 28856
243.75 28430
244.00 28495
244.25 28046
244.50 28446
244.75 29283
245.00 28294
245.25 28489
245.50 27937
245.75 27884
246.00 27894
246.25 27187
246.50 27607
246.75 27742
247.00 27002
247.25 27478
247.50 27347
247.75 27296
248.00 27211
248.25 27901
248.50 27883
248.75 27919
249.00 27840
249.25 27199
249.50 28084
249.75 27739
250.00 27779
250.25 28124
250.50 27791
250.75 28303
251.00 28267
251.25 27984
251.50 27825
251.75 27380
252.00 27853
252.25 27951
252.50 28274
252.75 27909
253.00 27720
253.25 28169
253.50 27876
253.75 28432
254.00 28022
254.25 28083
254.50 27913
254.75 27764
255.00 27959
255.25 28766
255.50 28007
255.75 28119
256.00 27233
256.25 27298
256.50 27435
256.75 28078
257.00 27602
257.25 28503
257.50 28340
257.75 28505
258.00 28292
258.25 28568
258.50 27781
258.75 28450
259.00 28154
259.25 28376
259.50 28699
259.75 28440
260.00 28562
260.25 27932
260.50 28230
260.75 28363
261.00 26915
261.25 27754
261.50 27634
261.75 27453
262.00 26051
262.25 26893
262.50 26419
262.75 25686
263.00 24660
263.25 24115
263.50 23535
263.75 22438
264.00 22414
264.25 21936
264.50 20895
264.75 20355
265.00 19227
265.25 18662
265.50 17662
265.75 17831
266.00 16906
266.25 16283
266.50 15240
266.75 15075
267.00 14331
267.25 13554
267.50 12955
267.75 12383
268.00 11671
268.25 11453
268.50 10724
268.75 10813
269.00 10045
269.25 9738
269.50 9017
269.75 9081
270.00 8412
270.25 8244
270.50 7546
270.75 7116
271.00 7388
271.25 7288
271.50 6844
271.75 7020
272.00 5994
272.25 5559
272.50 6094
272.75 6155
273.00 5678
273.25 5144
273.50 5751
273.75 5299
274.00 5140
274.25 4591
274.50 4398
274.75 4503
275.00 4386
275.25 4730
275.50 3924
275.75 4839
276.00 4564
276.25 4818
276.50 4686
276.75 4442
277.00 4502
277.25 3764
277.50 3912
277.75 4122
278.00 3833
278.25 4145
278.50 3257
278.75 3302
279.00 3989
279.25 3658
279.50 3677
279.75 3291
280.00 3169
280.25 3351
280.50 3507
280.75 3031
281.00 3568
281.25 3280
281.50 2693
281.75 3498
282.00 3539
282.25 2813
282.50 3337
282.75 3629
283.00 3671
283.25 3397
283.50 3265
283.75 3447
284.00 3723
284.25 3667
284.50 3363
284.75 3207
285.00 3599
285.25 3929
285.50 3088
285.75 3854
286.00 3111
286.25 4637
286.50 3481
286.75 3626
287.00 3999
287.25 4003
287.50 4016
287.75 4103
288.00 3841
288.25 4472
288.50 3984
288.75 3967
289.00 4236
289.25 4826
289.50 3935
289.75 4793
290.00 4948
290.25 5014
290.50 4990
290.75 4681
291.00 4941
291.25 5036
291.50 5673
291.75 5631
292.00 5257
292.25 5173
292.50 5120
292.75 5925
293.00 5874
293.25 5739
293.50 6418
293.75 6049
294.00 6819
294.25 6428
294.50 6965
294.75 6539
295.00 7223
295.25 7193
295.50 7289
295.75 7145
296.00 7860
296.25 7034
296.50 7947
296.75 7855
297.00 7826
297.25 8343
297.50 8045
297.75 8262
298.00 8214
298.25 8898
298.50 8869
298.75 9036
299.00 9058
299.25 9273
299.50 9470
299.75 9372
300.00 10123
300.25 10232
300.50 10588
300.75 10476
301.00 10421
301.25 10899
301.50 10675
301.75 11553
302.00 12226
302.25 12373
302.50 11669
302.75 11799
303.00 11768
303.25 12763
303.50 12499
303.75 12947
304.00 12455
304.25 13205
304.50 13304
304.75 13810
305.00 13765
305.25 14177
305.50 13727
305.75 14537
306.00 14907
306.25 14667
306.50 13791
306.75 14322
307.00 14974
307.25 15269
307.50 14801
307.75 14271
308.00 14585
308.25 14814
308.50 15501
308.75 15280
309.00 15065
309.25 15487
309.50 16007
309.75 15223
310.00 15317
310.25 15393
310.50 15001
310.75 15171
311.00 15865
311.25 15232
311.50 15691
311.75 15966
312.00 15178
312.25 15020
312.50 15261
312.75 15330
313.00 14969
313.25 14180
313.50 14313
313.75 14747
314.00 15029
314.25 14042
314.50 14005
314.75 14401
315.00 14527
315.25 14465
315.50 14569
315.75 13380
316.00 13779
316.25 13442
316.50 12755
316.75 13274
317.00 13217
317.25 12888
317.50 12656
317.75 12907
318.00 11747
318.25 11622
318.50 11107
318.75 12657
319.00 11435
319.25 11048
319.50 11277
319.75 11376
320.00 11352
320.25 10804
320.50 10115
320.75 10940
321.00 10708
321.25 9218
321.50 9199
321.75 9361
322.00 10483
322.25 9808
322.50 9237
322.75 9127
323.00 8536
323.25 8345
323.50 8869
323.75 8996
324.00 8674
324.25 7960
324.50 6887
324.75 7767
325.00 7403
325.25 7124
325.50 7100
325.75 7226
326.00 7963
326.25 7138
326.50 7450
326.75 7966
327.00 6804
327.25 7265
327.50 6958
327.75 6892
328.00 6125
328.25 6925
328.50 6225
328.75 5874
329.00 6435
329.25 5699
329.50 6238
329.75 6081
330.00 6214
330.25 6288
330.50 6524
330.75 5963
331.00 6309
331.25 5022
331.50 5653
331.75 5558
332.00 4839
332.25 4195
332.50 5042
332.75 4847
333.00 5598
333.25 5160
333.50 5348
333.75 5505
334.00 5079
334.25 5064
334.50 5206
334.75 5552
335.00 5344
335.25 6107
335.50 5144
335.75 5811
336.00 5558
336.25 4856
336.50 5630
336.75 4853
337.00 4757
337.25 5334
337.50 6131
337.75 5576
338.00 6005
338.25 5875
338.50 6029
338.75 6049
339.00 5440
339.25 6507
339.50 5764
339.75 5854
340.00 6422
340.25 6256
340.50 5712
340.75 5088
341.00 6609
341.25 5809
341.50 5687
341.75 5084
342.00 6450
342.25 6396
342.50 6161
342.75 6330
343.00 5875
343.25 5980
343.50 5821
343.75 6163
344.00 6060
344.25 6057
344.50 6029
344.75 6521
345.00 6258
345.25 5890
345.50 6329
345.75 5620
346.00 6275
346.25 5102
346.50 5641
346.75 5414
347.00 5347
347.25 4979
347.50 5688
347.75 5449
348.00 4640
348.25 5006
348.50 5004
348.75 4533
349.00 4231
349.25 6025
349.50 4685
349.75 3959
350.00 4212
350.25 4309
350.50 3600
350.75 3983
351.00 3823
351.25 3739
351.50 3855
351.75 3252
352.00 3630
352.25 3322
352.50 3826
352.75 3766
353.00 3259
353.25 3680
353.50 3229
353.75 3795
354.00 3080
354.25 2687
354.50 3047
354.75 2526
355.00 2853
355.25 2876
355.50 2526
355.75 2458
356.00 2430
356.25 2389
356.50 2323
356.75 2566
357.00 1905
357.25 2144
357.50 2414
357.75 2267
358.00 2510
358.25 2231
358.50 2307
358.75 1627
359.00 2008
359.25 2341
359.50 2120
359.75 1984
360.00 1981
360.25 1766
360.50 2014
360.75 1894
361.00 1608
361.25 1330
361.50 1772
361.75 1954
362.00 1534
362.25 1813
362.50 2317
362.75 1824
363.00 1853
363.25 1647
363.50 1450
363.75 1506
364.00 1239
364.25 1115
364.50 1609
364.75 1716
365.00 1414
365.25 2188
365.50 1337
365.75 1505
366.00 1327
366.25 1465
366.50 1375
366.75 1578
367.00 1455
367.25 1736
367.50 1549
367.75 1141
368.00 1540
368.25 1286
368.50 1629
368.75 1430
369.00 986
369.25 1971
369.50 1561
369.75 1652
370.00 1552
370.25 1478
370.50 1128
370.75 1454
371.00 1544
371.25 1100
371.50 1563
371.75 1547
372.00 1228
372.25 1687
372.50 1432
372.75 1442
373.00 1572
373.25 1705
373.50 1980
373.75 1379
374.00 1077
374.25 1272
374.50 1627
374.75 1238
375.00 1703
375.25 1619
375.50 1696
375.75 1234
376.00 1803
376.25 1549
376.50 1708
376.75 1269
377.00 1875
377.25 1509
377.50 1203
377.75 1880
378.00 1691
378.25 1627
378.50 1337
378.75 1374
379.00 1797
379.25 1690
379.50 1719
379.75 1823
380.00 1238
380.25 1535
380.50 1622
380.75 1342
381.00 2069
381.25 1201
381.50 1597
381.75 1892
382.00 1707
382.25 1555
382.50 2030
382.75 1438
383.00 1795
383.25 1862
383.50 1298
383.75 1283
384.00 1791
384.25 1811
384.50 1808
384.75 2012
385.00 1691
385.25 1419
385.50 1628
385.75 1701
386.00 1748
386.25 1643
386.50 1811
386.75 1937
387.00 1804
387.25 1545
387.50 2033
387.75 2033
388.00 1765
388.25 1874
388.50 2167
388.75 1899
389.00 1742
389.25 2070
389.50 2113
389.75 1852
390.00 1818
390.25 2238
390.50 2251
390.75 1560
391.00 1830
391.25 1906
391.50 2063
391.75 1944
392.00 2197
392.25 2062
392.50 2108
392.75 1921
393.00 1959
393.25 1762
393.50 2127
393.75 2080
394.00 1769
394.25 1954
394.50 2164
394.75 2027
395.00 2036
395.25 1958
395.50 2010
395.75 1839
396.00 1923
396.25 1881
396.50 2111
396.75 1943
397.00 2185
397.25 2018
397.50 1994
397.75 2208
398.00 1913
398.25 1900
398.50 2079
398.75 2080
399.00 2192
399.25 1892
399.50 1920
399.75 2165
400.00 1969
400.25 1828
400.50 1834
400.75 2291
401.00 2194
401.25 2056
401.50 2262
401.75 1963
402.00 2118
402.25 2052
402.50 1703
402.75 1523
403.00 1868
403.25 1833
403.50 1790
403.75 1954
404.00 2067
404.25 1800
404.50 1925
404.75 1857
405.00 1899
405.25 1999
405.50 1617
405.75 1705
406.00 1720
406.25 1790
406.50 1878
406.75 1860
407.00 1666
407.25 1526
407.50 1735
407.75 1748
408.00 1923
408.25 1903
408.50 1703
408.75 1620
409.00 1480
409.25 1597
409.50 1496
409.75 1518
410.00 1733
410.25 1657
410.50 1445
410.75 1643
411.00 1226
411.25 1427
411.50 1568
411.75 1442
412.00 1672
412.25 1632
412.50 1695
412.75 1568
413.00 1869
413.25 1779
413.50 1305
413.75 1716
414.00 1301
414.25 1366
414.50 1484
414.75 1370
415.00 1406
415.25 1779
415.50 1622
415.75 1601
416.00 1710
416.25 1540
416.50 1996
416.75 1298
417.00 1841
417.25 1560
417.50 1188
417.75 1518
418.00 1126
418.25 1150
418.50 1343
418.75 1265
419.00 1420
419.25 1578
419.50 1524
419.75 1187
420.00 1675
420.25 1202
420.50 1310
420.75 1583
421.00 1449
421.25 1704
421.50 1559
421.75 1407
422.00 1476
422.25 1327
422.50 1670
422.75 1464
423.00 1295
423.25 1478
423.50 1465
423.75 1874
424.00 1412
424.25 1469
424.50 1122
424.75 1380
425.00 1272
425.25 1553
425.50 1614
425.75 1774
426.00 1583
426.25 1174
426.50 1225
426.75 1469
427.00 1356
427.25 1656
427.50 1444
427.75 1170
428.00 1377
428.25 1342
428.50 1259
428.75 1481
429.00 1481
429.25 1452
429.50 1536
429.75 1351
430.00 1287
430.25 1387
430.50 1616
430.75 1291
431.00 1564
431.25 1649
431.50 1262
431.75 1494
432.00 1389
432.25 1471
432.50 1298
432.75 1272
433.00 1340
433.25 1354
433.50 1573
433.75 1525
434.00 1409
434.25 1618
434.50 1391
434.75 1399
435.00 1394
435.25 1930
435.50 1618
435.75 1619
436.00 1682
436.25 1708
436.50 1655
436.75 1204
437.00 1651
437.25 1647
437.50 1692
437.75 1711
438.00 1752
438.25 1880
438.50 1897
438.75 1810
439.00 1548
439.25 1793
439.50 1754
439.75 1878
440.00 1961
440.25 1889
440.50 1969
440.75 1917
441.00 2140
441.25 2068
441.50 2222
441.75 2073
442.00 2144
442.25 2112
442.50 2223
442.75 2156
443.00 2166
443.25 2453
443.50 2358
443.75 2345
444.00 2493
444.25 2412
444.50 2749
444.75 2357
445.00 2654
445.25 2473
445.50 2830
445.75 2965
446.00 2664
446.25 2732
446.50 2720
446.75 3127
447.00 3113
447.25 2906
447.50 2690
447.75 3124
448.00 3034
448.25 3149
448.50 3363
448.75 3305
449.00 3482
449.25 3667
449.50 3460
449.75 3474
450.00 3615
450.25 3749
450.50 3589
450.75 3743
451.00 3958
451.25 3956
451.50 3875
451.75 4228
452.00 4002
452.25 4233
452.50 4141
452.75 4063
453.00 4324
453.25 4468
453.50 4573
453.75 4428
454.00 4644
454.25 4601
454.50 4839
454.75 4740
455.00 4860
455.25 5032
455.50 5012
455.75 5129
456.00 5052
456.25 5259
456.50 5430
456.75 5208
457.00 5521
457.25 5603
457.50 5430
457.75 5529
458.00 5714
458.25 5810
458.50 5707
458.75 5672
459.00 6094
459.25 5989
459.50 6109
459.75 6450
460.00 6434
460.25 6585
460.50 6550
460.75 6502
461.00 6580
461.25 6738
461.50 6460
461.75 6770
462.00 6752
462.25 6950
462.50 6882
462.75 6922
463.00 6926
463.25 7261
463.50 7302
463.75 7372
464.00 7686
464.25 7643
464.50 7711
464.75 7690
465.00 7917
465.25 7651
465.50 8099
465.75 8134
466.00 8220
466.25 8478
466.50 8482
466.75 8613
467.00 8760
467.25 8943
467.50 8922
467.75 8904
468.00 9247
468.25 9506
468.50 9323
468.75 9480
469.00 9922
469.25 9790
469.50 9913
469.75 9983
470.00 10302
470.25 10346
470.50 10449
470.75 10679
471.00 10817
471.25 11168
471.50 11475
471.75 11491
472.00 11412
472.25 11951
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];
Once you are comfortable calculating the amount of light you'll detect learn about detection in the powerpoint below. This will help you let the optics be the limiting factor and not poor detection technique.
Powerpoint on Detection of Optical Confocal Signal
Additional files:
Noise analysis for PMT Matlab Code
%%%%NEP_PMT.m
%%%%%%%%%%Calculates NEP from PMT data
G=1e6; %%gain of the PMT
Ra=5e4; %%radiance responsivity of anode (A/W)
d=6; %%%secondary emission ratio
F=d/(d-1);
Ida=1e-9; %%anode dark current (A)
logB=[-2:1:8]; %%log of bandwidth in Hz
B=10.^(logB); %%bandwidth in Hz
e=1.6e-19; %%electronic charge (C)
NEP=e*G*F*B/(Ra)+((e*G*F*B).^2+4*e*Ida*G*F*B).^(0.5)/(Ra);
figure(2);clf
loglog(B,NEP,'linewidth',3.0)
hold on
plot(B,P1det+zeros(1,length(B)),'k--','linewidth',3.0)
xlabel('Bandwidth(Hz)','fontsize',14)
ylabel('NEP(W)','fontsize',14)
break
Gtia=1e5; %%TIA gain (Ohms=V/A);
NEP_I=NEP*Ra;
ENI=0.2e-9;
figure(3);clf
loglog(B,NEP_I,'linewidth',3.0)
hold on
plot(B,ENI+zeros(1,length(B)),'k--','linewidth',3.0)
xlabel('Bandwidth(Hz)','fontsize',14)
ylabel('current (A)','fontsize',14)
S=P1det*Ra*Gtia; %%%signal at the output of TIA
figure(4);clf
semilogx(B,S+zeros(1,length(B)),'k--','linewidth',3.0)
Noise analysis for DAQ Matlab Code
%%%DAQ_Noise.m
%%%%%%%%%%%%%%%%%%
bits=16; %%% number of bits
Vmax=0.2; %%%maximum voltage
% lsb=Vmax/(2^bits-1); %%%least significant bit
lsb=5.2e-6;
NEP_V=NEP*Ra*Gtia; %%%minimum input at detector S/N=1
figure(5);
loglog(B,NEP_V,'linewidth',3.0)
hold on
plot(B,lsb+zeros(1,length(B)),'k--','linewidth',3.0)
xlabel('Bandwidth(Hz)','fontsize',14)
ylabel('NEP at Daq(V)','fontsize',14)