Degrees of MEng, BEng and BSc in Engineering
ENG2088 Optical Engineering 2
Friday 28th April 2023. Release time: 0930一1100
Exam duration: 1.5 hours to complete exam plus 30 mins to upload submission
Total marks available 100 marks.
Attempt ALL questions.
• Write your student ID at the top of every page that you submit.
• The numbers in square brackets in the right-hand margin indicate the marks allotted to the part of the question against which the mark is shown. These marks are for guidance only.
• This is an open book exam and you may consult your notes and any other available reference material. However, you are advised against directly copying from lecture slides or published materials.
• Marks will be awarded on the basis of understanding and application of the subject. Therefore candidates should ensure their answers show all intermediate steps and as- sumptions in calculations. Answers given without relevant working or justification will receive partial marks only.
• A computational device or calculator may be used.
• Although you can discuss how to approach the exam, and revise with other students, you must not discuss specific exam questions or answers with other students. This is collusion and will result in conduct action.
Q1. A symmetrical biconvex lens with a focal length of 40mm is used to image an object 25mm from the lens
(a) The refractive index of the lens material is 1.6, hence find the radius of curvature of the spherical lens surface. You can assume the thin lens approximation.
(b) Draw a ray diagram of this optical setup.
(c) Is the image real or virtual?
(d) Is the image upright or inverted?
(e) Where is the position of the image?
(f) What is the magnification of the image?
(g) It is observed that image from a large diameter lens of this specification is degraded (blurred) when compared to a small diameter lens with otherwise the same specifica- tion. What is the cause of this aberration?
Q2. The James Webb Space Telescope (JWST) is currently deployed to make observations primarily in the infrared spectrum. It has a 6.5m diameter primary mirror with a focal length of 131.4m. In this question we consider the hypothetical case where the primary mirror is the only focusing element.
(a) What is the f-number for the JWST primary mirror?
(b) Approximating a circular aperture, a point source (star) images to an Airy diffraction pattern. What is the diameter of the Airy disk (to first irradiance minimum) at the imaging sensor for a near-IR wavelength of λ = 2.0 μm?
(c) The NIRCam imaging sensor for this near-IR wavelength uses 2040 × 2040 sensor arrays with the imaging area measuring 1.63m on each side. Is the resolution of the image limited by diffraction or the pixel dimension?
(d) Calculate the angular field-of-view of this single imaging sensor.
Figure Q2: Plot of the function J1(x)/x, where J1(x) is a Bessel function of the first kind.
Q3. Zinc Selenide (ZnSe) is often used in the optics of infrared instruments, such as those on the JWST. It has a refractive index of 2.44 at a wavelength of λ = 2.0 μm, which is to be used throughout this question.
(a) What is the critical angle for total internal reflection? [3]
(b) What is the reflectivity (irradiance) at normal incidence from a ZnSe surface in vac-uum? [4]
(c) Explain what Brewster’s angle corresponds to. [4]
(d) What is the value of Brewster’s angle for incident light on a ZnSe surface in vacuum? [5]
Q4. At the exit facet of a cleaved optical fibre, the emitted light into air at a wavelength of 1300nm can be approximated with a transverse Gaussian irradiance profile with a e2/1 diameter of 5 μm and a flat phase-front.
(a) What is the Rayleigh range for this optical beam? [4]
(b) What is the far-field Numerical Aperture (NA) for this optical beam? [4]
(c) A ×40 microscope objective is used to collimate this optical beam. What is the focal length of the objective? [4] It is a standard microscope objective for a compound microscope based on the standard 160mm tube length.
(d) What consideration should be made regarding the Numerical Aperture of the micro-scope objective to ensure the beam retains its transverse Gaussian irradiance profile? [3]
(e) Calculate the e2/1 irradiance diameter of the collimated beam immediately following the microscope objective. [4]
(f) The cleaved end of the fibre is modified, such that the exit facet takes a convex form. and the light is emitted with the same transverse Gaussian irradiance profile, but now with a curved phase-front. Sketch a diagram that indicates the subsequent change to the beam propagation in air. [6]
Q5. The gap between two pieces of industrial machinery is monitored by using it in one arm of a Michelson interferometer, with the other arm being of fixed length. The interferometer uses a red laser of wavelength λ = 650nm. Table Q5 shows the time of day after which the specified number of whole fringes have emerged at the centre of the interference pattern. Determine an estimate for the rate of change of the gap. You may use graph paper, spreadsheet or mathematical computing software to calculate providing you include it in your upload. [18]
Table Q5: Recorded time of day when specified number of fringes have emerged in pattern