User:Pranav Rathi/Notebook/OT/2012/11/13/Optical Tweezers Calibration - Revision history

Pranav Rathi: /* Method */

2012-11-25T04:52:39Z

Method

←Older revision		Revision as of 04:52, 25 November 2012
Line 166:		Line 166:
	* I use bead from Bang’s labs [http://www.bangslabs.com/products/o/list/ProActive%20Protein%20Coated%20Microspheres/CP01N/63]. Material is polystyrene with refractive index of 1.2 in water, density 1.06 g/cm<sup>3</sup>, radius either 520nm or 261 nm, mass either 6.24e-13 or 7.89e-14 g.		* I use bead from Bang’s labs [http://www.bangslabs.com/products/o/list/ProActive%20Protein%20Coated%20Microspheres/CP01N/63]. Material is polystyrene with refractive index of 1.2 in water, density 1.06 g/cm<sup>3</sup>, radius either 520nm or 261 nm, mass either 6.24e-13 or 7.89e-14 g.
	* Sample preparation in H<sub>2</sub>O:		* Sample preparation in H<sub>2</sub>O:
-	1μl of bead (1:50) + 3μl of BGB in H<sub><sup>2</sup></sub>0=4μl of bead (1:200)	+	1μl of bead (1:50) + 3μl of BGB in H<sub><sup>2</sup></sub>O=4μl of bead (1:200)

-	2μl of bead (1:50) + 10μl of BGB in H<sub><sup>2</sup></sub>0=12μl of bead (1:1200)	+	2μl of bead (1:50) + 10μl of BGB in H<sub><sup>2</sup></sub>O=12μl of bead (1:1200)

	In D<sub>2</sub>O		In D<sub>2</sub>O

-	1μl of bead (1:50) + 3μl of BGB in D<sub><sup>2</sup></sub>0=4μl of bead (1:200)	+	1μl of bead (1:50) + 3μl of BGB in D<sub><sup>2</sup></sub>O=4μl of bead (1:200)

-	2μl of bead (1:50) + 10μl of BGB in D<sub><sup>2</sup></sub>0=12μl of bead (1:1200)	+	2μl of bead (1:50) + 10μl of BGB in D<sub><sup>2</sup></sub>O=12μl of bead (1:1200)

	To determine the stiffness I need corner frequency. To know the corner frequency I do a power-spectrum of position signal of a freely trapped bead in the x-direction (x-signal from ontrack). This gives me a one sided Lorentzian on a log-log plot (magnitude Vs frequency). To get the corner frequency I fit this data with power-spectrum equation; fit gives me relative magnitude, corner frequency and variance. This is done by ''Power-spectrum module'' built in ''feedback96_main program''. I use RMS averaging, linear weighting mode and hanning window. The dependence of the cutoff frequency is measured on two quantities:		To determine the stiffness I need corner frequency. To know the corner frequency I do a power-spectrum of position signal of a freely trapped bead in the x-direction (x-signal from ontrack). This gives me a one sided Lorentzian on a log-log plot (magnitude Vs frequency). To get the corner frequency I fit this data with power-spectrum equation; fit gives me relative magnitude, corner frequency and variance. This is done by ''Power-spectrum module'' built in ''feedback96_main program''. I use RMS averaging, linear weighting mode and hanning window. The dependence of the cutoff frequency is measured on two quantities:

Pranav Rathi: /* Method */

2012-11-25T03:24:55Z

Method

←Older revision		Revision as of 03:24, 25 November 2012
Line 167:		Line 167:
	* Sample preparation in H<sub>2</sub>O:		* Sample preparation in H<sub>2</sub>O:
	1μl of bead (1:50) + 3μl of BGB in H<sub><sup>2</sup></sub>0=4μl of bead (1:200)		1μl of bead (1:50) + 3μl of BGB in H<sub><sup>2</sup></sub>0=4μl of bead (1:200)
		+
	2μl of bead (1:50) + 10μl of BGB in H<sub><sup>2</sup></sub>0=12μl of bead (1:1200)		2μl of bead (1:50) + 10μl of BGB in H<sub><sup>2</sup></sub>0=12μl of bead (1:1200)

	In D<sub>2</sub>O		In D<sub>2</sub>O
		+
	1μl of bead (1:50) + 3μl of BGB in D<sub><sup>2</sup></sub>0=4μl of bead (1:200)		1μl of bead (1:50) + 3μl of BGB in D<sub><sup>2</sup></sub>0=4μl of bead (1:200)
		+
	2μl of bead (1:50) + 10μl of BGB in D<sub><sup>2</sup></sub>0=12μl of bead (1:1200)		2μl of bead (1:50) + 10μl of BGB in D<sub><sup>2</sup></sub>0=12μl of bead (1:1200)

Pranav Rathi: /* Method */

2012-11-25T03:24:14Z

Method

←Older revision		Revision as of 03:24, 25 November 2012
Line 166:		Line 166:
	* I use bead from Bang’s labs [http://www.bangslabs.com/products/o/list/ProActive%20Protein%20Coated%20Microspheres/CP01N/63]. Material is polystyrene with refractive index of 1.2 in water, density 1.06 g/cm<sup>3</sup>, radius either 520nm or 261 nm, mass either 6.24e-13 or 7.89e-14 g.		* I use bead from Bang’s labs [http://www.bangslabs.com/products/o/list/ProActive%20Protein%20Coated%20Microspheres/CP01N/63]. Material is polystyrene with refractive index of 1.2 in water, density 1.06 g/cm<sup>3</sup>, radius either 520nm or 261 nm, mass either 6.24e-13 or 7.89e-14 g.
	* Sample preparation in H<sub>2</sub>O:		* Sample preparation in H<sub>2</sub>O:
-	~~2ul~~ of bead (1:50) + ~~10ul~~ of BGB in H<sub><sup>2</sup></sub>0=~~12ul~~ of bead (1:~~250~~)	+	1μl of bead (1:50) + 3μl of BGB in H<sub><sup>2</sup></sub>0=4μl of bead (1:200)
		+	2μl of bead (1:50) + 10μl of BGB in H<sub><sup>2</sup></sub>0=12μl of bead (1:1200)

	In D<sub>2</sub>O		In D<sub>2</sub>O
-		+	1μl of bead (1:50) + 3μl of BGB in D<sub><sup>2</sup></sub>0=4μl of bead (1:200)
-	~~2ul~~ of bead (1:50) +~~10ul~~ of BGB in ~~d2o~~=~~12ul~~ of bead (1:~~250~~)	+	2μl of bead (1:50) + 10μl of BGB in D<sub><sup>2</sup></sub>0=12μl of bead (1:1200)

	To determine the stiffness I need corner frequency. To know the corner frequency I do a power-spectrum of position signal of a freely trapped bead in the x-direction (x-signal from ontrack). This gives me a one sided Lorentzian on a log-log plot (magnitude Vs frequency). To get the corner frequency I fit this data with power-spectrum equation; fit gives me relative magnitude, corner frequency and variance. This is done by ''Power-spectrum module'' built in ''feedback96_main program''. I use RMS averaging, linear weighting mode and hanning window. The dependence of the cutoff frequency is measured on two quantities:		To determine the stiffness I need corner frequency. To know the corner frequency I do a power-spectrum of position signal of a freely trapped bead in the x-direction (x-signal from ontrack). This gives me a one sided Lorentzian on a log-log plot (magnitude Vs frequency). To get the corner frequency I fit this data with power-spectrum equation; fit gives me relative magnitude, corner frequency and variance. This is done by ''Power-spectrum module'' built in ''feedback96_main program''. I use RMS averaging, linear weighting mode and hanning window. The dependence of the cutoff frequency is measured on two quantities:

Pranav Rathi: /* results */

2012-11-24T21:31:02Z

results

←Older revision		Revision as of 21:31, 24 November 2012
Line 177:		Line 177:
	* Trap height-the distance from the center of the trap to the surface of the coverglass- which affects the dynamic viscosity of the surrounding water and it may also affect the trap stuffiness by changing the amount of aberration (but I do not worry about this too much because we have correction color on our objective to reduce this effect)		* Trap height-the distance from the center of the trap to the surface of the coverglass- which affects the dynamic viscosity of the surrounding water and it may also affect the trap stuffiness by changing the amount of aberration (but I do not worry about this too much because we have correction color on our objective to reduce this effect)

-	===~~results~~===	+	===Results===

	[[Category:Construction of Optical Tweezers and devices]]		[[Category:Construction of Optical Tweezers and devices]]

Pranav Rathi: /* Method */

2012-11-24T21:21:37Z

Method

←Older revision		Revision as of 21:21, 24 November 2012
Line 162:		Line 162:

	===Method===		===Method===
		+
		+	The calibration requires free beads. I make samples with dilute suspension of the beads in deionized water. Some facts about the beads:
		+	* I use bead from Bang’s labs [http://www.bangslabs.com/products/o/list/ProActive%20Protein%20Coated%20Microspheres/CP01N/63]. Material is polystyrene with refractive index of 1.2 in water, density 1.06 g/cm<sup>3</sup>, radius either 520nm or 261 nm, mass either 6.24e-13 or 7.89e-14 g.
		+	* Sample preparation in H<sub>2</sub>O:
		+	2ul of bead (1:50) + 10ul of BGB in H<sub><sup>2</sup></sub>0=12ul of bead (1:250)
		+
		+	In D<sub>2</sub>O
		+
		+	2ul of bead (1:50) +10ul of BGB in d2o=12ul of bead (1:250)
		+
		+	To determine the stiffness I need corner frequency. To know the corner frequency I do a power-spectrum of position signal of a freely trapped bead in the x-direction (x-signal from ontrack). This gives me a one sided Lorentzian on a log-log plot (magnitude Vs frequency). To get the corner frequency I fit this data with power-spectrum equation; fit gives me relative magnitude, corner frequency and variance. This is done by ''Power-spectrum module'' built in ''feedback96_main program''. I use RMS averaging, linear weighting mode and hanning window. The dependence of the cutoff frequency is measured on two quantities:
		+
		+	* Laser power, which is directly proportional to cutoff frequency. I know the laser power from the AOM RF-input voltage.
		+	* Trap height-the distance from the center of the trap to the surface of the coverglass- which affects the dynamic viscosity of the surrounding water and it may also affect the trap stuffiness by changing the amount of aberration (but I do not worry about this too much because we have correction color on our objective to reduce this effect)
		+
		+	===results===

	[[Category:Construction of Optical Tweezers and devices]]		[[Category:Construction of Optical Tweezers and devices]]

Pranav Rathi: /* Background */

2012-11-24T20:31:46Z

Background

←Older revision		Revision as of 20:31, 24 November 2012
Line 160:		Line 160:

	If the bead is too close to the surface (h<10 times the bead radius) in drag coefficient Faxen’s term dominates, and reports a wrong corner frequency (hens wrong stiffness). So when I do power-spectrum I make sure that I am more than 10 times of bead radius away from the surface. This affect can be exploited to determine the height of the bead correctly above the surface. If I know the corner frequency way away from the surface I can calculate it at any height from the surface; for example when bead center is a radius away from the surface the corner frequency would be 1/3. So knowing the corner frequency precisely I can position the bead precisely above the surface. This can help me knowing the trap height above the surface. But just remember the bead center and trap center do not coincide; due to the scattering force the equilibrium position for the bead center is slightly away from the trap center in the z-direction., which can be calibrated and since i am using water immersion objective with correction color i do not have to worry about the focal shift.		If the bead is too close to the surface (h<10 times the bead radius) in drag coefficient Faxen’s term dominates, and reports a wrong corner frequency (hens wrong stiffness). So when I do power-spectrum I make sure that I am more than 10 times of bead radius away from the surface. This affect can be exploited to determine the height of the bead correctly above the surface. If I know the corner frequency way away from the surface I can calculate it at any height from the surface; for example when bead center is a radius away from the surface the corner frequency would be 1/3. So knowing the corner frequency precisely I can position the bead precisely above the surface. This can help me knowing the trap height above the surface. But just remember the bead center and trap center do not coincide; due to the scattering force the equilibrium position for the bead center is slightly away from the trap center in the z-direction., which can be calibrated and since i am using water immersion objective with correction color i do not have to worry about the focal shift.
		+
		+	===Method===

	[[Category:Construction of Optical Tweezers and devices]]		[[Category:Construction of Optical Tweezers and devices]]

Pranav Rathi: /* Background */

2012-11-24T20:31:00Z

Background

←Older revision		Revision as of 20:31, 24 November 2012
Line 159:		Line 159:
	</math>		</math>

-	If the bead is too close to the surface (h<10 times the bead radius) in drag coefficient Faxen’s term dominates, and reports a wrong corner frequency (hens wrong stiffness). So when I do power-spectrum I make sure that I am more than 10 times of bead radius away from the surface. This affect can be exploited to determine the height of the bead correctly above the surface. If I know the corner frequency way away from the surface I can calculate it at any height from the surface; for example when bead center is a radius away from the surface the corner frequency would be 1/3. So knowing the corner frequency precisely I can position the bead precisely above the surface. This can help me knowing the trap height above the surface. But just remember the bead center and trap center do not coincide; due to the scattering force the equilibrium position for the bead center is slightly away from the trap center in the z-direction., which can be calibrated.	+	If the bead is too close to the surface (h<10 times the bead radius) in drag coefficient Faxen’s term dominates, and reports a wrong corner frequency (hens wrong stiffness). So when I do power-spectrum I make sure that I am more than 10 times of bead radius away from the surface. This affect can be exploited to determine the height of the bead correctly above the surface. If I know the corner frequency way away from the surface I can calculate it at any height from the surface; for example when bead center is a radius away from the surface the corner frequency would be 1/3. So knowing the corner frequency precisely I can position the bead precisely above the surface. This can help me knowing the trap height above the surface. But just remember the bead center and trap center do not coincide; due to the scattering force the equilibrium position for the bead center is slightly away from the trap center in the z-direction., which can be calibrated and since i am using water immersion objective with correction color i do not have to worry about the focal shift.

	[[Category:Construction of Optical Tweezers and devices]]		[[Category:Construction of Optical Tweezers and devices]]

Pranav Rathi: /* Background */

2012-11-24T20:21:18Z

Background

←Older revision		Revision as of 20:21, 24 November 2012
Line 157:		Line 157:
	\beta=\frac{6\pi\eta r}		\beta=\frac{6\pi\eta r}
	{1-\frac{9}{16}(\frac{r}{h})+\frac{1}{8}(\frac{r}{h})^3-\frac{45}{256}(\frac{r}{h})^4-\frac{1}{16}(\frac{r}{h})^5}		{1-\frac{9}{16}(\frac{r}{h})+\frac{1}{8}(\frac{r}{h})^3-\frac{45}{256}(\frac{r}{h})^4-\frac{1}{16}(\frac{r}{h})^5}
-
	</math>		</math>
		+
	If the bead is too close to the surface (h<10 times the bead radius) in drag coefficient Faxen’s term dominates, and reports a wrong corner frequency (hens wrong stiffness). So when I do power-spectrum I make sure that I am more than 10 times of bead radius away from the surface. This affect can be exploited to determine the height of the bead correctly above the surface. If I know the corner frequency way away from the surface I can calculate it at any height from the surface; for example when bead center is a radius away from the surface the corner frequency would be 1/3. So knowing the corner frequency precisely I can position the bead precisely above the surface. This can help me knowing the trap height above the surface. But just remember the bead center and trap center do not coincide; due to the scattering force the equilibrium position for the bead center is slightly away from the trap center in the z-direction., which can be calibrated.		If the bead is too close to the surface (h<10 times the bead radius) in drag coefficient Faxen’s term dominates, and reports a wrong corner frequency (hens wrong stiffness). So when I do power-spectrum I make sure that I am more than 10 times of bead radius away from the surface. This affect can be exploited to determine the height of the bead correctly above the surface. If I know the corner frequency way away from the surface I can calculate it at any height from the surface; for example when bead center is a radius away from the surface the corner frequency would be 1/3. So knowing the corner frequency precisely I can position the bead precisely above the surface. This can help me knowing the trap height above the surface. But just remember the bead center and trap center do not coincide; due to the scattering force the equilibrium position for the bead center is slightly away from the trap center in the z-direction., which can be calibrated.

	[[Category:Construction of Optical Tweezers and devices]]		[[Category:Construction of Optical Tweezers and devices]]

Pranav Rathi: /* Background */

2012-11-24T20:20:33Z

Background

←Older revision		Revision as of 20:20, 24 November 2012
Line 151:		Line 151:
	K=2\pi\beta f_c		K=2\pi\beta f_c
	</math>		</math>
-	~~Stiffness depends on the corner frequency f<sub>c</sub> and drag coefficient. Drag coefficent plays an important role~~

		+	Stiffness depends on the corner frequency f<sub>c</sub> and drag coefficient. Drag coefficient plays an important role in corner frequency determination, because it is height dependent. If the bead is too close to the surface the drag coefficient will change to Faxen’s law:

		+	:<math>
		+	\beta=\frac{6\pi\eta r}
		+	{1-\frac{9}{16}(\frac{r}{h})+\frac{1}{8}(\frac{r}{h})^3-\frac{45}{256}(\frac{r}{h})^4-\frac{1}{16}(\frac{r}{h})^5}
		+
		+	</math>
		+	If the bead is too close to the surface (h<10 times the bead radius) in drag coefficient Faxen’s term dominates, and reports a wrong corner frequency (hens wrong stiffness). So when I do power-spectrum I make sure that I am more than 10 times of bead radius away from the surface. This affect can be exploited to determine the height of the bead correctly above the surface. If I know the corner frequency way away from the surface I can calculate it at any height from the surface; for example when bead center is a radius away from the surface the corner frequency would be 1/3. So knowing the corner frequency precisely I can position the bead precisely above the surface. This can help me knowing the trap height above the surface. But just remember the bead center and trap center do not coincide; due to the scattering force the equilibrium position for the bead center is slightly away from the trap center in the z-direction., which can be calibrated.

	[[Category:Construction of Optical Tweezers and devices]]		[[Category:Construction of Optical Tweezers and devices]]

Pranav Rathi: /* Electronic filters */

2012-11-22T04:22:37Z

Electronic filters

←Older revision		Revision as of 04:22, 22 November 2012
Line 99:		Line 99:
	I use Krohn-Hite single-ended input 8-pole low-pass Bessel filters with cutoff at 1.5 kHz for x, y, sum and piezo signal. Even though the filters have cutoff at 1.5 kHz but they affect the power-spectrum generated corner frequency even at 500Hz. I use x-signal from on-track to generate the power-spectrum.		I use Krohn-Hite single-ended input 8-pole low-pass Bessel filters with cutoff at 1.5 kHz for x, y, sum and piezo signal. Even though the filters have cutoff at 1.5 kHz but they affect the power-spectrum generated corner frequency even at 500Hz. I use x-signal from on-track to generate the power-spectrum.
	[[Image:Krohn-Hite filter rolloff.jpg\|right\|300x200px]]		[[Image:Krohn-Hite filter rolloff.jpg\|right\|300x200px]]
-	To study this behavior I generate an interferogram of sound with frequency components from 10 to 1600 Hz with ''whitesoundmain'' program written in labview V9 and produce it at the ~~soundcard~~ output of one computer. I feed this sound into mic-input of another computer and read the interferogram with ''Noise investigator and helper'' program written in labview V9 (I used the same programs and method to study structural resonance of optical setups). See the slide show for more information.	+	To study this behavior I generate an interferogram of sound with frequency components from 10 to 1600 Hz with ''whitesoundmain'' program written in labview V9 and produce it at the output of soundcard of one computer. I feed this sound signal into mic-input of another computer and read the interferogram with ''Noise investigator and helper'' program written in labview V9 (I used the same programs and method to study structural resonance of optical setups). See the slide show for more information.

	I record the data; when there was no filter between the output and input (signal goes straight from one computer to another) and when there is a filter between (signal goes through the filter before input). The result is as expected: Graph is a power spectrum of input interferogram; without filter (Red curve) it is a square function over 1600Hz, with filter (white curve) frequency starts rolling off after 360Hz. This means with filter on power-spectrum taken at frequencies higher than 360Hz will report false corner frequency (low corner frequency will report low stiffness).		I record the data; when there was no filter between the output and input (signal goes straight from one computer to another) and when there is a filter between (signal goes through the filter before input). The result is as expected: Graph is a power spectrum of input interferogram; without filter (Red curve) it is a square function over 1600Hz, with filter (white curve) frequency starts rolling off after 360Hz. This means with filter on power-spectrum taken at frequencies higher than 360Hz will report false corner frequency (low corner frequency will report low stiffness).