1. a) Given the transfer function of a detector (below), label and describe these terms: i. dynamic range ii. linear dynamic range iii. sensitivity iv. responsivity b) Imagine you are using an optical detector to characterize the output power of a light source with increasing voltage. If you assumes that your detector response is linear in the range at which you are taking measurements, but in fact your output changes non-linearly with your incident radiant power how will this affect the interpretation of your measured data? You won t be able to measure the incident power precisely. The readout of the power would be lower than the real incident power. c) In the above experiment, you are taking the measurement in the lab with all the lights on. Even worse, the AC just broke down and the room temperature reaches about 80 F. Please list all possible sources that can induce inaccuracy in your measurements. Compare their differences and how you can eliminate or reduce them. 1. Noises, including shot noise and thermal noise. You can lower the noise by cooling the system down or taking averages. 2. Background. Turn off the light or use black curtain.
2. Please use your drawing to illustrate how PMT and APD work and compare the mechanisms which enable them to achieve signal amplification. Also, explain why is it hard to make a detector that has high detectivity while also preserves a high detection speed? Working mechanism: Please check the slides In order to achieve high detectivity, you need detector with larger area. This will increase the capacity of your detecting system and increase your response time of the detector. 3. You are assigned a project to measure water concentration in a rat burn wound model using an optical technique. In this technique, you project light onto the sample and capture the reflected light from the wound using a photodetector. You purchase a 25mW short wave infrared LED with FWHM of 27nm centered at 1450 nm. This peak wavelength is close to a peak in water absorption spectra. Your next step is to choose a photodetector with a sensitive material. Which semiconductor material do you choose among Si (1.12 ev), GaP (2.26 ev), GaN (3.44eV), and InAs (0.36eV)? Please provide quantitative proof for your decision. Incident Light Energy E = hc/λ E = (6.626*10-34 Js)(3*10 8 m/s)/(1450*10-9 m) = 0.87 ev Band Gap: Si: 1.12, InAs: 0.36, GaN: 3.44, GaP: 2.26 ev E > Band Gap photoelectric effect Choose InAs 4. Say that we take an optical fiber with indices of refraction of 1.450 and 1.436, with a core
radius of a=50µm. (a) Which index is the core and which is the cladding? (b) If this were a step index fiber (in air), calculate the numerical aperture and maximum acceptance angle. (c) What is the effective f/# of the step index fiber? (d) Say that we want to couple light from the step index fiber into a detector. Take a lens with a focal length of +25 mm and diameter 5 mm. What is the f/# of this lens? (e) Place the fiber at the focal point of this lens and align the center of the fiber with the center of the lens. Will all of the light from the fiber couple into this lens?
5. a) Please label the type of the fibers and explain how you identify them. b) Plot how the output pulse would look like for each fiber. Explain how the structures of the fiber affect the pulses coming out of the fiber. We differentiate the single- and multi- mode fiber based on the size of the core. The GRIN fiber we can tell based on the refractive index map. The output pulse; check the lecture slides 6. Compare the optical sectioning effect of two photon excited fluorescence microscopy to confocal fluorescence microscopy. List the pros and cons of each imaging technology. TPEF, self-sectioning you can have depth information without the need of a pin hole. Confocal, use a pin hole.
TPEF, simple configuration, better penetration depth, less photo damage. The cost is much higher than confocal due to the need of a special laser. Confocal, need to use pin hole, lower penetration depth. Low cost and easy to implement. Provides high resolution. 7. Please explain how the magnification and NA of the objective affect the resolution of the system. The magnification doesn t affect the system resolution. The higher the NA the better the resolution. 8. You have laser scanning microscope equipped with a 20x dry objective (NA=0.55), a 40x dry objective (NA = 0.8), a 60x dry objective (NA = 0.95) and a 60x water immersion objective (f# = 0.74). The system has a 380 nm continuous laser source with 400mW power, a 490 nm continuous laser source with 100mW power, 780 nm continuous laser source with 800mW power, a 770nm 150 fs pulsed laser and 200mW power. Which laser source and objective would you chose for the following situations and why. a) Study the metabolic activities in breast cancer cells especially the activities in mitochondria. The mitochondria are stained with Rhodamine. b) Image a non-stained skin biopsy from a melanoma patient. c) A time elapse study of embryo development (last for 48 hours). The cells are stained with DAPI. Rhodamine spectrum Rhodamine spectrum DAPI spectrum a) Use 60x dry objective, since it provides the highest NA thus best spatial resolution. Use 490nm laser source since it matches with the absorption peak of Rhodamine.
b) Use 20X dry objective, it has lower NA thus longer working distance enable us to image deeper. Use 770nm 150fs laser, as longer wavelength allows for deeper imaging depth. Also, the excitation matches the absorption peak of NADH c) Use 60x dry objective and 380nm CW laser or 770nm fs laser. Want stable signal, thus use dry objective. 380nm can excite DAPI most efficiently.