Blackbody-wavelength of the infrared emission

Question

Question 1: For a blackbody, the frequency at which maximum energy is emitted is 3 x 10¹³ Hz:

A) Give a wave number for the wavelength of the infrared emission?

B) Determine the temperature of the blackbody?

C) Determine the total radiance emittance for the blackbody?

D) Consider  an  emitter  (with  an  emissivity  of  0.5)  at  similar  temperature  of  the blackbody (obtained from B). Find out the total power lost by this emitter if its area is 2 m² ?

Question 2: Infra-Red Detectors and Optic Lens

Part A: An IR detector has an impedance of Z= (400 + j200) Ω. During the design tests the detector current is measured as 4 µA. Determine the output voltage of the detector?

Part B: By using a converging lens of focal length f = 10 cm, we want an object to appear on the screen twice as big as its original size. Where is the object to be placed in front of the screen (real image)?

Question 3: Digital Image

Part A: Determine the raw file size for an image of 80 rows and 100 columns, with pixels on 14 bits and with an extra row for the header?

Part B: The minimum and maximum values observed in the low-contrast 12-bit thermogram are 60 and 250, correspondingly. A pixel in the thermogram has been mapped to a new value of 4000 after linear stretching. Determine the value of the pixel before stretching?

Part C: Regarding filtering, image masking and convolution. Suppose we have the given Infra-Red image:

What filter would you use to remove the impulsive noise in the first row of the image (suppose 1 x 3 filter)?

What would the first row of the image be after filtering (suppose 1 x 3 filter)?