Optical Locating - Revision history

EricN: /* Phase-Sensitive Detection Circuit */

2009-01-07T03:13:48Z

Phase-Sensitive Detection Circuit

← Older revision		Revision as of 22:13, 6 January 2009
Line 30:		Line 30:

	==Phase-Sensitive Detection Circuit==		==Phase-Sensitive Detection Circuit==
	The ~~difficulty~~ in trying to identify a target which could be buried within background ambient light is differentiating between the ambient signal and the target signal. The method of achieving that separation that this system uses is called [[Phase-Sensitive Detection\|phase-sensitive-detection]]. The phase sensitive detection starts with modulating the signal voltage at a certain frequency. It is then multiplied by a reference signal at the same frequency. The multiplication can be carried out in a sectional called mixer, or in other ways. The phase sensitive detection ends with a low pass filter, which demodulates the signal voltage and outputs a DC value.		The most difficult part of trying to identify a target which could be buried within background ambient light is differentiating between the ambient signal and the target signal. The method of achieving that separation that this system uses is called [[Phase-Sensitive Detection\|phase-sensitive-detection]]. The phase sensitive detection starts with modulating the signal voltage at a certain frequency. It is then multiplied by a reference signal at the same frequency. The multiplication can be carried out in a sectional called mixer, or in other ways. The phase sensitive detection ends with a low pass filter, which demodulates the signal voltage and outputs a DC value.

Zhao: /* Phase-Sensitive Detection Circuit */

2008-12-13T04:08:45Z

Phase-Sensitive Detection Circuit

← Older revision		Revision as of 23:08, 12 December 2008
Line 30:		Line 30:

	==Phase-Sensitive Detection Circuit==		==Phase-Sensitive Detection Circuit==
	The difficulty in trying to identify a target which could be buried within background ambient light is differentiating between the ambient signal and the target signal. The method of achieving that separation that this system uses is called [[Phase-Sensitive Detection\|phase-sensitive-detection]].		The difficulty in trying to identify a target which could be buried within background ambient light is differentiating between the ambient signal and the target signal. The method of achieving that separation that this system uses is called [[Phase-Sensitive Detection\|phase-sensitive-detection]]. The phase sensitive detection starts with modulating the signal voltage at a certain frequency. It is then multiplied by a reference signal at the same frequency. The multiplication can be carried out in a sectional called mixer, or in other ways. The phase sensitive detection ends with a low pass filter, which demodulates the signal voltage and outputs a DC value.

EricN at 19:41, 12 December 2008

2008-12-12T19:41:35Z

← Older revision		Revision as of 14:41, 12 December 2008
Line 15:		Line 15:
	* [[IR Target Illumination\|Target illumination circuit]]		* [[IR Target Illumination\|Target illumination circuit]]
	* [[Optics]]		* [[Optics]]
	* Phase-sensitive detection circuit		* [[Phase-Sensitive Detection\|Phase-sensitive detection circuit]]
	* Microcontroller		* Microcontroller

EricN at 19:41, 12 December 2008

2008-12-12T19:41:03Z

← Older revision		Revision as of 14:41, 12 December 2008
Line 2:		Line 2:

	===Overview===		===Overview===
			<b> This page still needs more revision and completeness, but the individual technologies are fully developed </b>

	Many tracking applications require that the system identify the location of information within a visual field. This could be seeking a color, or a shape, or just the centroid of light intensity. This page discusses the use of a duo-lateral photodiode to sense the centroid of light within its field of view. The documented method uses a passive [[Sensing optical tape\|retro-reflective]] target and [[Optics\|optics]].		Many tracking applications require that the system identify the location of information within a visual field. This could be seeking a color, or a shape, or just the centroid of light intensity. This page discusses the use of a duo-lateral photodiode to sense the centroid of light within its field of view. The documented method uses a passive [[Sensing optical tape\|retro-reflective]] target and [[Optics\|optics]].
Line 11:		Line 12:

	* Eye structure on a 2-DoF gimbal		* Eye structure on a 2-DoF gimbal
	* Position-sensing detector		* [[Lateral-Effect Photodiode\|Position-sensing detector]]
	* Target illumination circuit		* [[IR Target Illumination\|Target illumination circuit]]
	* Optics		* [[Optics]]
	* Phase-sensitive detection circuit		* Phase-sensitive detection circuit
	* Microcontroller		* Microcontroller

Zhao: /* Phase-Sensitive Detection Circuit */

2008-12-11T23:35:41Z

Phase-Sensitive Detection Circuit

← Older revision		Revision as of 18:35, 11 December 2008
Line 29:		Line 29:

	==Phase-Sensitive Detection Circuit==		==Phase-Sensitive Detection Circuit==
	The difficulty in trying to identify a target which could be buried within background ambient light is differentiating between the ambient signal and the target signal. The method of achieving that separation that this system uses is called [[Phase-Sensitive Detection\|phase-sensitive-detection]]. Essentially, the circuit uses an active low-pass filter to compare the centroid of light with the illumination on to the centroid of light with the illumination off, by switching from one lead when the illumination is on to the other when it is off. The use of the other lead when the illumination is off allows the filter to compare		The difficulty in trying to identify a target which could be buried within background ambient light is differentiating between the ambient signal and the target signal. The method of achieving that separation that this system uses is called [[Phase-Sensitive Detection\|phase-sensitive-detection]].

	'''Overview'''

	One effective way to recover the small signal buried by large ambient noise is to use the so called phase sensitive detector, or lock-in amplifier. A phase sensitive detector achieves narrow bandwidth amplification by reducing the noise content at falling outside the interested bandwidth.

	When the noise is white in nature, we can reduce its level of magnitude dramatically by limiting the bandwidth of detection, which includes the frequency occurring to the signal while excludes the frequencies occurring to the noise. Phase sensitive detection enables extremely narrow bandwidth detection (0.001Hz is normal). Typical application scenario is using electric transducers where the amplitude of noise is in mili volts and the signal falls into nano volt region. Sophisticated phase sensitive detector can extract signals buried in noise that is 107 times larger in magnitude.

	In this article, we focus on a quick and easy method of building a phase sensitive detector from op-amps and analog switches.

	'''Mathematical model'''

	Consider two signals, <math>f_1</math> and <math>f_2</math>, where <math>f_1=Asin\omega_1 t</math> , <math>f_2=Bsin(\omega_2 t + \phi)</math>

	Then, the product of <math>f_1</math> and <math>f_2</math> is:


	<math>f_1\times f_2 = ABsin\omega_1 tsin(\omega_2 t + \phi) </math>
	<math>= -\frac{AB}{2} \times {cos[(\omega_1 + \omega_2 )t+\phi ]-cos[(\omega_1 - \omega_2 )t-\phi ]}</math>

	Let’s integrate the product over time <math>[0, T)</math>:

	<math>\frac{1}{T} \int_{0}^{T}f_1\times f_2\, dt</math>
	<math>=\frac{1}{T} \int_{0}^{T}-\frac{AB}{2} \times \{ cos[(\omega_1 + \omega_2 )t+\phi ]-cos[(\omega_1 - \omega_2 )t-\phi ]\} \, dt</math>
	<math>= -\frac{AB}{2T} \int_{0}^{T} cos[(\omega_1 + \omega_2 )t+\phi ] \,dt + \frac{AB}{2T} \int_{0}^{T} cos[(\omega_1 - \omega_2 )t-\phi ] \,dt </math>

	When <math> T \to \infty </math> , both parts are equal to 0, except when <math>\omega_1 = \omega_2 </math> and <math>\phi = 0</math>, the integration result is equal to <math>\frac{AB}{2}</math> .


	As can be observed, only signals in phase, in other words, sharing the same frequency and phase angle, will result in a non-zero value after multiplication and integration. This indicates a way to recover the signal from noise: by modulating the interesting signal and doing the maths.This is the mathematical foundation of phase sensitive detection, because all signals can be broken down in to several harmonic components.


	'''Method'''

	A phase sensitive detection can be split into 6 stages:

	1. Modulation: Modulate the signal at a certain frequency.

	2. Pre-amplification: A high-speed amplifier required to amplify the signal (along with the noise) to a suitable level for succeeding circuit. We can also stick in a high pass filter (can be a capacitor) after amplification, just to eliminate the DC portion of the noise.

	3. Reference circuit: Usually a pulse wave at the modulating frequency, which can be from a function generator, or a 555 timer, or PIC, etc.

	4. Multiplier: At this stage, we multiply the pre-amplified signal (along with the noise) with the reference signal. One easy way to do multiplication is suggested here: we use the reference signal to turn on and off an analog switch periodically, and let the modulated input signal pass the analog switch. So when the switch is ON (meaning connected to the input pin of the integrator), the output is ‘<math>input \times 1</math>’, and when the switch is OFF (meaning connected to the ground), the output is ‘<math>input \times 0</math>’.

	5. Integrator (demodulation): Let the multiplied signal pass through an integrator. The multiplied signal can have a lot of components – almost all of them will become zero after integration (see explanation in the mathematical model), but the one which is the product of the modulated signal and the reference signal will remain, because they are at the same frequency and the same phase angle. This is the essence of phase sensitive detection – only the product of the two signals that are ‘in phase’ will remain after integration. ‘In phase’ means the two signals share common frequency and phase angle. We can also do amplification at the integration stage by sticking in a feedback resistor (see the example circuit diagram), just for convenience.

	6. Low pass filter: After integration, the signal is recovered and demodulated to a DC output. However, it may not be a perfect DC voltage due to high frequency spikes that still exist. That’s why the low pass filter come into play.

	'''Example circuit diagram'''

	The concept of phase sensitive detection has been proved effective in optical tracking with lateral effect photodiode. The following circuit picks up the difference of the two corresponding output pins of the photodiode, in order to tell the position of the centroid of IR light on the photodiode sensing surface. The connection for the Y+ and Y- pins of the photodiode is exactly the same with what’s shown here for X+ and X-. The timer is realized by a 555 chip, and the chip for analog switch is Maxim 4056.
	[[Image:schematic of phase sensitive detection.jpg]]



	'''Commercial phase sensitive detectors'''

	This link below provides some useful information on commercially available phase sensitive detectors, or lock-in amplifiers.

	[http://www.thinksrs.com/products/SR810830.htm]SRS series Lock-in amplifiers

Zhao: /* Phase-Sensitive Detection Circuit */

2008-12-11T22:41:53Z

Phase-Sensitive Detection Circuit

← Older revision		Revision as of 17:41, 11 December 2008
Line 58:		Line 58:


	As can be observed, only signals in phase -- in other words, sharing the same frequency and phase angle will result in a non-zero value after multiplication and integration. This indicates a way to recover the signal from noise: by modulating the interesting signal and doing the maths.This is the mathematical foundation of phase sensitive detection, because all signals can be broken down in to several harmonic components.		As can be observed, only signals in phase, in other words, sharing the same frequency and phase angle, will result in a non-zero value after multiplication and integration. This indicates a way to recover the signal from noise: by modulating the interesting signal and doing the maths.This is the mathematical foundation of phase sensitive detection, because all signals can be broken down in to several harmonic components.

Zhao: /* Phase-Sensitive Detection Circuit */

2008-12-11T22:40:23Z

Phase-Sensitive Detection Circuit

← Older revision		Revision as of 17:40, 11 December 2008
Line 71:		Line 71:
	3. Reference circuit: Usually a pulse wave at the modulating frequency, which can be from a function generator, or a 555 timer, or PIC, etc.		3. Reference circuit: Usually a pulse wave at the modulating frequency, which can be from a function generator, or a 555 timer, or PIC, etc.

	4. Multiplier: At this stage, we multiply the pre-amplified signal (along with the noise) with the reference signal. One easy way to do multiplication is suggested here: we use the reference signal to turn on and off an analog switch periodically, and let the modulated input signal pass the analog switch. So when the switch is ON (meaning connected), the output is ‘<math>input \times 1</math>’, and when the switch is OFF (meaning ~~disconnected~~), the output is ‘<math>input \times 0</math>’.		4. Multiplier: At this stage, we multiply the pre-amplified signal (along with the noise) with the reference signal. One easy way to do multiplication is suggested here: we use the reference signal to turn on and off an analog switch periodically, and let the modulated input signal pass the analog switch. So when the switch is ON (meaning connected to the input pin of the integrator), the output is ‘<math>input \times 1</math>’, and when the switch is OFF (meaning connected to the ground), the output is ‘<math>input \times 0</math>’.

	5. Integrator (demodulation): Let the multiplied signal pass through an integrator. The multiplied signal can have a lot of components – almost all of them will become zero after integration (see explanation in the mathematical model), but the one which is the product of the modulated signal and the reference signal will remain, because they are at the same frequency and the same phase angle. This is the essence of phase sensitive detection – only the product of the two signals that are ‘in phase’ will remain after integration. ‘In phase’ means the two signals share common frequency and phase angle. We can also do amplification at the integration stage by sticking in a feedback resistor (see the example circuit diagram), just for convenience.		5. Integrator (demodulation): Let the multiplied signal pass through an integrator. The multiplied signal can have a lot of components – almost all of them will become zero after integration (see explanation in the mathematical model), but the one which is the product of the modulated signal and the reference signal will remain, because they are at the same frequency and the same phase angle. This is the essence of phase sensitive detection – only the product of the two signals that are ‘in phase’ will remain after integration. ‘In phase’ means the two signals share common frequency and phase angle. We can also do amplification at the integration stage by sticking in a feedback resistor (see the example circuit diagram), just for convenience.

Zhao: /* Phase-Sensitive Detection Circuit */

2008-12-11T22:39:14Z

Phase-Sensitive Detection Circuit

← Older revision		Revision as of 17:39, 11 December 2008
Line 71:		Line 71:
	3. Reference circuit: Usually a pulse wave at the modulating frequency, which can be from a function generator, or a 555 timer, or PIC, etc.		3. Reference circuit: Usually a pulse wave at the modulating frequency, which can be from a function generator, or a 555 timer, or PIC, etc.

	4. Multiplier: At this stage, we multiply the pre-amplified signal (along with the noise) with the reference signal. One easy way to do multiplication is suggested here: we use the reference signal to turn on and off an analog switch periodically, and let the modulated input signal pass the analog switch. So when the switch is ON (meaning connected), the output is ‘<math>input /times 1</math>’, and when the switch is OFF (meaning disconnected), the output is ‘<math>input \times 0</math>’.		4. Multiplier: At this stage, we multiply the pre-amplified signal (along with the noise) with the reference signal. One easy way to do multiplication is suggested here: we use the reference signal to turn on and off an analog switch periodically, and let the modulated input signal pass the analog switch. So when the switch is ON (meaning connected), the output is ‘<math>input \times 1</math>’, and when the switch is OFF (meaning disconnected), the output is ‘<math>input \times 0</math>’.

	5. Integrator (demodulation): Let the multiplied signal pass through an integrator. The multiplied signal can have a lot of components – almost all of them will become zero after integration (see explanation in the mathematical model), but the one which is the product of the modulated signal and the reference signal will remain, because they are at the same frequency and the same phase angle. This is the essence of phase sensitive detection – only the product of the two signals that are ‘in phase’ will remain after integration. ‘In phase’ means the two signals share common frequency and phase angle. We can also do amplification at the integration stage by sticking in a feedback resistor (see the example circuit diagram), just for convenience.		5. Integrator (demodulation): Let the multiplied signal pass through an integrator. The multiplied signal can have a lot of components – almost all of them will become zero after integration (see explanation in the mathematical model), but the one which is the product of the modulated signal and the reference signal will remain, because they are at the same frequency and the same phase angle. This is the essence of phase sensitive detection – only the product of the two signals that are ‘in phase’ will remain after integration. ‘In phase’ means the two signals share common frequency and phase angle. We can also do amplification at the integration stage by sticking in a feedback resistor (see the example circuit diagram), just for convenience.

Zhao: /* Phase-Sensitive Detection Circuit */

2008-12-11T22:38:43Z

Phase-Sensitive Detection Circuit

← Older revision		Revision as of 17:38, 11 December 2008
Line 71:		Line 71:
	3. Reference circuit: Usually a pulse wave at the modulating frequency, which can be from a function generator, or a 555 timer, or PIC, etc.		3. Reference circuit: Usually a pulse wave at the modulating frequency, which can be from a function generator, or a 555 timer, or PIC, etc.

	4. Multiplier: At this stage, we multiply the pre-amplified signal (along with the noise) with the reference signal. One easy way to do multiplication is suggested here: we use the reference signal to turn on and off an analog switch periodically, and let the modulated input signal pass the analog switch. So when the switch is ON (meaning connected), the output is ~~‘input~~  1’, and when the switch is OFF (meaning disconnected), the output is ~~‘input~~  0’.		4. Multiplier: At this stage, we multiply the pre-amplified signal (along with the noise) with the reference signal. One easy way to do multiplication is suggested here: we use the reference signal to turn on and off an analog switch periodically, and let the modulated input signal pass the analog switch. So when the switch is ON (meaning connected), the output is ‘<math>input /times 1</math>’, and when the switch is OFF (meaning disconnected), the output is ‘<math>input \times 0</math>’.

	5. Integrator (demodulation): Let the multiplied signal pass through an integrator. The multiplied signal can have a lot of components – almost all of them will become zero after integration (see explanation in the mathematical model), but the one which is the product of the modulated signal and the reference signal will remain, because they are at the same frequency and the same phase angle. This is the essence of phase sensitive detection – only the product of the two signals that are ‘in phase’ will remain after integration. ‘In phase’ means the two signals share common frequency and phase angle. We can also do amplification at the integration stage by sticking in a feedback resistor (see the example circuit diagram), just for convenience.		5. Integrator (demodulation): Let the multiplied signal pass through an integrator. The multiplied signal can have a lot of components – almost all of them will become zero after integration (see explanation in the mathematical model), but the one which is the product of the modulated signal and the reference signal will remain, because they are at the same frequency and the same phase angle. This is the essence of phase sensitive detection – only the product of the two signals that are ‘in phase’ will remain after integration. ‘In phase’ means the two signals share common frequency and phase angle. We can also do amplification at the integration stage by sticking in a feedback resistor (see the example circuit diagram), just for convenience.

Zhao: /* Headline text */

2008-12-11T22:37:10Z

Headline text

← Older revision		Revision as of 17:37, 11 December 2008
Line 45:		Line 45:
	Then, the product of <math>f_1</math> and <math>f_2</math> is:		Then, the product of <math>f_1</math> and <math>f_2</math> is:


	== Headline text ==
	<math>f_1\times f_2 = ABsin\omega_1 tsin(\omega_2 t + \phi) </math>		<math>f_1\times f_2 = ABsin\omega_1 tsin(\omega_2 t + \phi) </math>
	<math>= -\frac{AB}{2} \times {cos[(\omega_1 + \omega_2 )t+\phi ]-cos[(\omega_1 - \omega_2 )t-\phi ]}</math>		<math>= -\frac{AB}{2} \times {cos[(\omega_1 + \omega_2 )t+\phi ]-cos[(\omega_1 - \omega_2 )t-\phi ]}</math>