University of Toronto Edward S. Rogers Sr. Department of Electrical and Computer Engineering

ECE318 – Fundamentals of Optics

Lab #4 INTRODUCTION TO OPTICAL IMAGE PROCESSING

CAUTION: ● NEVER LOOK DIRECTLY INTO A LASER BEAM. IT IS HARMFUL TO

YOUR EYES. ● NEVER TOUCH THE SURFACES OF OPTICAL ELEMENTS. ● HANDLE ALL OPTICAL ELEMENTS WITH CARE.

Apparatus:

1 JDSU He-Ne Laser (632.8nm) 1528P-0 ● Power: 0.5 mW ● Beam diameter: 0.48mm, ● Beam divergence: 1.7 mrad

2 Edmund Spatial Filter Movement Stage

NT39-976

3 Edmund Microscope Objective 40X

DIN NT43-904

4 Edmund Precision Pinhole 15 µm NT38-

540

5 SORL 15 in (380 mm) focal length; f/5

lenses; achromatic-doublets designed for 632.8 nm He-Ne laser light

6 Metrological Transparency Slides 45-

673

7 Edmund Iris NT53-914

8 Adjustable mechanical slit

9 Viewing screen

Background In this lab, we perform optical signal processing on images generated by illuminating slides with specific aperture functions (Fig. 1). When illuminated, light is transmitted and diffracted through the aperture opening and completely blocked otherwise. On the observation plane, the amplitude of the electric field at the aperture is described by E(x,y).

Figure 1. Diffraction of light at an aperture According to Huygens-Fresnel principle, the diffraction of light at an aperture is equivalent to the sum of the waves produced by spherical points sources located at every point of the aperture. At an observation plane that is at a distance z away from the aperture, the diffracted wave pattern A(x’,y’) can be described as:

𝐴 𝑥#, 𝑦# = '()

𝐸 𝑥, 𝑦 +,-.

/0𝑑𝑥𝑑𝑦,2

32 (1)

Object plane

Observation plane

E(x,y) A(x’,y’)

x

y

x’

y’

z

where λ is the wavelength of the incident light, 𝑘 = 2𝜋/𝜆 is the wavenumber, and 𝑟 =(𝑥 − 𝑥′)> + (𝑦 − 𝑦′)> + (𝑧)>.

If we are only interested in the intensity of the diffraction pattern and assume that the observation plane is located at infinity (Fraunhofer approximation), equation (1) can be re-written and simplified as:

𝐴 𝜐B, 𝜐C = 𝑒𝑖𝑘𝑧

𝑖𝜆𝑧𝑒𝑖𝜋𝜆(𝜐𝑥

2+𝜐𝑦2) 𝐸 𝑥, 𝑦 𝑒(>F(BGHICGJ)𝑑𝑥𝑑𝑦,232 (2)

where 𝜐B =

B#)' and 𝜐C =

C#)'

. From equation (2), it is observed that the far-field diffraction pattern 𝐴 𝜐B, 𝜐C is proportional to the 2D Fourier transform of the incident field𝐸 𝑥, 𝑦 . Specifically, 𝜐Band 𝜐C are called spatial frequency, the frequency with which the brightness modulates across space. Of course, equation (2) is only valid when the observation distance is large. Such requirement can be eliminated by inserting the illuminated object at the front focal plane of a lens (z = F). The lens effectively introduces a quadratic phase factor (𝑒3

,0LMN (B

0IC0)) onto the diffracted wave such that the Fourier transform of the aperture will occur at the back focal plane the lens, given by:

𝐴 𝜐B, 𝜐C = 1𝑖𝜆𝐹

𝐸 𝑥, 𝑦 𝑒(>F(BGHICGJ)𝑑𝑥𝑑𝑦232 . (3)

Thus, the thin lens allows us to observe and measure the Fourier transform in close proximity. An example is shown in Fig. 2. Here, spatial frequency corresponds to the number of times the dark (or transparent) lines are repeated per unit distance. When the slide is illuminated, a column of bright dots can be observed at the back focal plane of the lens (Fourier plane). The brightest dot in the middle of the Fourier transform is the DC term, representing the average brightness of the object. The spatial frequency increases away from the center of the Fourier plane.

Figure 2. Fourier transform of gratings via a thin lens.

A(νy) E(y)

FT

In this experiment, we utilized the Fourier transform property of a lens for optical image processing. The optical set-up is shown in Fig. 3 and the basic steps are:

1. An object is illuminated with a collimated laser light with low spatial noise (cleaned using pin hole and microscope objective).

2. A lens is used to perform a spatial Fourier Transform of the image. 3. Spatial frequency filtering is carried out at the Fourier plane by employing

appropriate spatial filters to block the desired frequencies. 4. The final image is reconstructed by an additional lens which performs another

Fourier Transform on the filtered image located at the Fourier plane.

Figure 3. Optical arrangement for image processing.

Procedure: (1) Cleaning the Illumination Beam via Spatial Filtering Before performing optical image processing, it is necessary to reduce the spatial intensity noise on the laser beam that will be illuminating the imaging object. This noise generally has high spatial frequency contents that are produced by the scattering of various imperfections in the optical beam path. This noise can be eliminated by first use a microscope objective lens to tightly focus the collimated He-Ne laser beam. Then, small pinhole is placed at the focal plane of the objective lens and centered onto the beam. The pinhole filters out the high spatial frequency contents and effectively “cleans up” the He-Ne beam. CAUTION: ● Do not touch the delicate surface of the pinhole foil - it is expensive and tears

easily. ● Make sure the objective does not come into contact with the pinhole foil!

Laser

1. Place the white viewing screen after the He-Ne laser and observe the beam profile. Describe the appearance of the beam.

2. Carefully carry out the following steps to align the pinhole to the focal point of the microscope objective lens (Fig. 4). This is not easy to do, and requires careful and patient adjustment of all three axes of the spatial filtering stage that supports the pinhole:

Figure 4. Spatial filter movement stage set-up

i. Move the objective as far away from the pinhole as possible using the Z

adjustment micrometer knob of the spatial filter stage.

ii. Make sure the laser is off. Remove both the pinhole and the objective from the stage.

iii. Turn the laser on. Observe and mark where the laser beam hits the screen.

iv. Put the objective back and use the X and Y controls of the component

holder to achieve the following a. The laser passes through the centre of the objective. b. Light that diffracts from the objective is centered on the mark on the

screen.

v. Put the pinhole back. Slowly move the objective forward until a small disk of light passes through the pinhole onto the screen. If the disk is not centered on the mark, adjust the X and Y control of the spatial filter stage. The disk will move in the same direction as the X and Y adjustments.

Spatial filter stage

Component holder

Z-adjustment

XY-adjustment

Tilt-adjustment

vi. Continue to slowly move the objective forward and adjust the pinhole position. If the disk disappears, move the objective away from the pinhole until it appears again and resume the process.

vii. The intensity of the disk will grow as you move closer to the focal point. If you are close to the focal point, rings will become visible around the blob of light (due to diffraction from the edge of the pinhole).

viii. Stop when the rings merge with the disk and an intense, symmetric beam pattern is observed on the screen.

ix. Note that if the disk starts to move in the opposite direction as the X and Y

adjustments, you have overshot.

3. Describe any changes in the appearance of the beam and explain the change. (2) Collimation Once the laser beam has been cleaned, a lens (L1) is used to collimate and expand the beam such that the imaging object can be fully illuminated (Fig. 3).

1. Position the collimating lens one focal lens away from the pinhole. Note that the two faces of the lens have different focal length (35 cm or 36.3 cm). Check the focal length of the lenses using the methods outlined in lab 1. Make sure the center of the lens is aligned with the center of the pinhole. Aberrations are minimized when the most curved surface (smallest radius) of the lens faces the collimated beam.

2. Check the collimation by observing the output beam diameter on the viewing screen

over a distance of several meters – the diameter should be relatively constant. If not, then adjust the longitudinal position of the collimating lens.

(3) Spatial Fourier Transform by a Lens: A lens performs a spatial Fourier Transform of the field distribution pattern at the object plane onto its focal plane (the Fourier plane). If a transparent slide with a printed image is placed on the object plane, the uniform intensity of the illumination beam is modified by the printed image. Consequently, the pattern at the Fourier plane (back focal plane of the lens) is changed. In this part of the lab, you are asked to place several different slides in the object plane to spatially modulate the uniform light beam. Predict how the pattern at the Fourier plane should appear.

1. Place a slide holder in front of lens L1. Place another lens L2 at a distance of one focal length away from the slide holder as shown in Fig 1. Place the viewing screen at the back focal plane of lens L2.

2. Place images of linear gratings (slides 4) at the object plane (Fig. 5), and record your observations of the Fourier images. Change the orientation of the gratings and describe the changes in the Fourier plane. Repeat with slides 5 and 6.

Figure 5. Images of linear gratings

3. Place images of grids (slides 10) at the object plane (Fig. 6), and record your

observations of the Fourier images. Repeat with slides 11 and 12.

Figure 6. Images of grids

4. Explain what is seen in the Fourier plane by considering the following:

Given a line-to-line spacing, d, grating interference maxima occur for specific angles satisfying the grating formula:

𝑚𝜆 = 𝑑 sin 𝜃 (4)

In the Fourier plane of lens L2, these peaks should be separated by ~𝑓> tan 𝜃 from the optical axis (y’=x’=0). The focal length of lens L2 is approximately 𝑓>=35mm. Use these relations, calculate where the spatial frequencies for slide 4 should appears on the Fourier plane.

5. From your observations in the previous steps, make a general, qualitative

conclusion regarding the dependence of the image observed at the Fourier plane on the spatial frequencies of the original slide image at the object plane.

(4) Optical Image Processing: Fourier optics principles can be used for optical image processing. The processing allows us to accentuate or eliminate certain elements of an image. Specifically, spatial filters (low-pass, high-pass, or band-pass) are applied to remove some of the spatial frequencies before reconstructing the image through another Fourier transform. This can be done since spatial

Slide 4 Slide 5 Slide 6

Slide 10 Slide 11 Slide 12

frequencies are increases radially outward. Moreover, spatial frequencies in different directions on the original image are also oriented in different directions on the Fourier plane.

1. Use lens L3 to reconstruct the image (Fig. 3). Place it at one focal length away from the Fourier plane. Place the viewing screen behind L3 at the image plane.

To check the optical set-up, use an object with fine structure such as slide 14. Make small adjustments to the lens and screen positions to obtain maximum visibility of the fine structure.

2. Using slides 13, 14, and 21 (Fig. 6), perform the following experiment:

Place one slide in the object plane, and place a variable iris in the Fourier Plane. Make sure the iris is mounted on a component mount with XYZ control. Properly center the iris with respect to the DC component on the Fourier plane. Observe the change in the image on the screen as you gradually close down the variable iris. Record and briefly explain your observations.

Repeat the above for the other two slides.

Figure 6. Images of slides with more than one spatial frequency.

3. Typically cloud chamber photographs include a large number of relatively parallel

tracks of incoming particles, and a few curved tracks caused by interactions. By filtering in the Fourier plane, we can change the relative intensities of these features in the image. Use slide 22, a cloud chamber photograph (Fig. 7). Close down the iris in the Fourier plane and observe the image when the iris is on-axis (centred on the DC component) and off-axis. Describe any changes to the image when the iris is closed.

Slide 13 Slide 14 Slide 21

Figure 7. Cloud chamber photograph

4. Repeat step 3 with adjustable mechanical slit instead of the iris. Adjust the height,

rotation, and width of the slit to filter out the DC component and record your observation (draw a sketch of the Fourier-plane observations and then overlay with a drawing of the optical filter). Readjust the slit such that the DC component can now pass through and record your observations. Explain your observations. Discuss the pros and cons of using the iris or the adjustable slit for optical image processing.

CAUTION: Do not apply excessive force to the pins as they bend and break easily.

5. Use the slide of a sailing boat (Fig. 8). Orient the adjustable slit such that everything but the grid appearing in the sail is filtered out. Repeat the process for the grid in the boat, the grid in the water, etc.

Figure 8. Sailing boat slide.

6. If the distance between two grids on the sailing boat slide is 0.5 mm, use equation (4) and calculate the minimum slit width for filtering.

Reference:

● Class notes and “Introduction to Optics” Chapter 21, by Pedrotti, 3rd edition. ● Edmund Optics: understand spatial filter:

https://www.edmundoptics.com/resources/application-notes/lasers/understanding-spatial-filters/