Vietnam

Interferometer

A good example of the interference phenomenon is the various colors in soap bubbles and floating oil. An interferometer uses the phenomenon to measure length and analyze light spectrum.

 

An interferometer splits light from a light source into two beams. One beam strikes either a flat, high-precision orientation plate, which is used for measurement and exhibits an irregularity of no more than 30 nm, or a reference plate having a reference lens coating, which is used for measuring spherical surfaces. The beam is then reflected. The other beam is transmitted through the reference plate, then strikes the measurement specimen. It too is then reflected. The light reflected from the reference plate and the light reflected from the measurement specimen return back along the original optical paths. Interference fringes are generated due to the optical path differences. The appearance of the fringes permits measurements of the surface configuration of the specimen and the shape of the transmitted wavefront.

Spacing between Fringes

One special feature of an interferometer is the high level of precision because it use light wavelengths as the standard of length. Observed bright/dark fringes appear as contour lines. Spacing between these lines is determined by the wavelength of the light source and the angle of incidence.

 

Ordinarily, the beam would strike perpendicular to the target surface, and in that case the spacing between the contour lines would be half the wavelength. But if it strikes at an angle, the contour lines spread out in proportion to the angle of incidence—in other words, there is low sensitivity.

The fringes shown on the screen are contour lines representing approximately 0.3 μm height intervals from the reference lens. If the sphericalness of the target surface is extremely good, the fringes are straight lines, and with adjustments there will be no fringes appears.

 

Starting at the zero fringe state, when the Left/Right dial of the five-axis adjustment base is turned a little, vertical fringes appear. When the Back/Forth dial is slightly turned, horizontal diverger lens interference fringes appear. And, when the Up/Down dial of the five-axis adjustment base is turned a little, concentric fringes appear.

Results when a test specimen with good sphericalness is shifted Left/Right

When the surface accuracy of a measurement specimen is excellent, the entire surface exhibits the same brightness, and when the specimen is tilted, equidistant straight fringes appear at right angles to the direction of the tilt.

 

When the spherical surface of a test specimen has a slight irregularity, the fringes bend. The greater the bend, the greater is the irregularity.

Result when a test spherical surface with considerable irregularity is shifted Left/Right

If the measurement specimen has a gently spherical surface, unevenly spaced concentric fringes appear, and when the specimen is tilted the concentric center shifts.

We offer a variety types of interferometers, each one designed for specific purposes. Here, we will introduce our typical interferometers used for surface profile measurements.

Fizeau Interferometer

This interferometer uses a laser light source. It has a simple structure and can measure flat and spherical surfaces with high precision, making it the most widely distributed of all interferometers. After the laser beam passes through the diverger lens, beam splitter and collimator lens, the rays become parallel. They strike the high-precision transmission plate (a flat glass plate).

 

Part of the light striking the transmission plate is reflected by the reference surface (the surface at the bottom of the transmission plate), while the remaining light passes through the transmission plate, strikes the surface of the measured target, and then is reflected. The light reflected from the reference surface and the target measured surface return back along the original optical paths. Interference fringes are generated due to the optical path differences.

 

*The reference surface is polished to a high level of precision, so that it exhibits an irregularity of less than 30 nm. This irregularity on the reference surface can be imagined as equivalent to less than that of one ping-pong ball sitting on a completely flat surface the size of the Kanto Plain in Japan.
*The Kanto Plain has an area of approximately 17,000 km2 which is about the same as that of Shikoku (18,297.78 km2).

Fizeau Interferometer Structure

Fizeau Interferometer for Flat Surface Measurements (Compact Laser Interferometer F601 (Flat surface measurement))

Fizeau Interferometer for Flat Surface Measurements (Laser Interferometer G102)

Fizeau Interferometer for Spherical Surface Measurement

As the above illustration shows, a reference lens is used instead of a transmission plate. This makes it possible to measure spherical surfaces. The final surface of the reference lens has a spherical shape polished to a high level of precision. It becomes the reference surface. Here, too, the reference surface is a means to split the light into two parts. Therefore, the laser light strikes the reference surface at a right angle. Part of the light is reflected, while the remaining is emitted at a right angle and strikes the measured surface (spherical surface).

 

When the location of the measured surface (the distance between the reference surface and the measured surface) is adjusted so that the light emitted from the reference surface strikes the measured surface at a right angle, the light from the measured surface returns along its original path, interfering with the light reflected from the reference surface. This makes it possible to measure the surface configuration of the measured surface. Furthermore, when the light emitted from the reference surface is focused on one point on the measured surface (generally called the cat’s eye point shown in the illustration, the measured surface is the location indicated by the broken line), the reflected light’s wavefront turns 180 degrees and returns to the reference lens, interfering with the light reflected from the reference surface. This makes it possible to observe interference fringes. The fringes can be observed only when the measured surface is placed at these two points. At any other location, the fringes would be too muted, for all practical purposes, to be observed. Measuring the distance between these two points makes it possible to obtain the curvature radius (R) of the measured surface. The illustration shows a situation where the concave surface is measured. To measure a convex surface, it is necessary to place the measured surface between the cat’s eye point and the reference surface.

Fizeau Interferometer for Spherical Surface Measurements (Compact laser interferometer F601 (Spherical surface measurement))

Compact laser interferometer F601 (spherical measurement) system is a Fizeau interferometer with a 60 mm diameter aperture for measuring spherical surfaces.

Reference Lenses for the F601 Interferometer

From among our eight types of reference lenses, you can select the one that best suits your requirements for measuring spherical surface profiles with different apertures and curvature radius. The reference surfaces of our reference lenses are generally with accuracy better than λ/20.

 

 

Measurement range (curvature radius) (mm)

Maximum measurement diameter (mm)

F No.

Reference lens curvature radius (mm)

Convex

Concave

Convex

Concave

0.6

17

2 - 17

3 - 103

27

120

0.7

23

3 - 23

4 - 97

32

120

1.0

43

5 - 43

7 - 77 (130)

40

72 (120)

1.4

65

9 - 65

14 - 75 (170)

46

53 (120)

2.0

105

16 - 105

31 - 38 (255)

53

19 (120)

2.8

150

30 (0) - 150

- (0 - 210)

53

- (75)

5.6

270

150 (125) - 270

- (0 - 90)

48

- (16)

8.0

442

320 (90) - 440

55

  • Shown are approximate values when the thickness of the measured lens is considered as zero.

  • Values in parentheses ( ) in the table are measurable range when a special stand was used.

  • Please contact us when the curvature radius of measured lens is close to zero.

An interferogram provides a rough estimation of the shape and flatness (or sphericity) of a the measured surface. But to obtain high precision surface profiles, a special analyzer is required.

 

An interference fringe analyzer captures CCD fringe images to a computer, obtains the phases for each point of light, and then computes the shapes. A number of methods can be used for phase computation. Here we will look briefly at the fringe scan method and the Fourier transform method.

Fringe Scan Method

Fringes obtained with an interferometer are generally brightness photos which vary as sinusoid waves. Therefore, if you know the brightness at the points being observed, you can learn the initial phase at those points, and obtain the optical path differences (height information). However, image shading and noise make it difficult to determine brightness and initial phase from one fringe image. The fringe scan method was developed to accurately obtain the initial phase.


Shifting the reference surface or the measured surface slightly in the direction of the optical axis will change the spacing between them, permitting the observation of fringe changes. The overall shapes of the fringes do not actually change, but when you look closely at individual points you will see how the brightness changes cyclically as the fringes are scanned.

 

When the fringes are scanned for exactly one cycle (2π), the spacing between the reference surface and the measured surface changes. During this time, for each fringe scan at π/2 (one-quarter of one fringe) interval, four different interferograms are captured (taking the four-step method as an example), and the initial phase is calculated from changes in the brightness. When the brightness at an observed point exhibits changes in the order of I0, I1, I2 and I3, the initial phase (Φ) can be expressed as follows:

However, Φ is wrapped into a value between –π and π, so if there is a phase jump of 2π at neighboring points, it becomes necessary to add or subtract 2π in order to connect the phases. This operation is called phase unwrapping.

 

If Φ is calculated for all points and the results are connected, you can obtain data for all phases. Then, when this data is transformed into lengths, you can obtain the shape.

To perform a fringe scan, the reference surface is mechanically shifted using a piezo element, so you will need to attach a dedicated fringe scan adaptor to the interferometer.

 

In addition to the above-mentioned 4-step algorithm, a number of other algorithms have been developed for the fringe scan method, including 3-, 5- and 7-step algorithms etc. Each algorithm has its own special characteristics, but any one of them can be applied to high-precision measurements.

 

 

Below are four captured images for each π/2, phases calculated from those images, and a bird’s eye view showing the result of phase unwrapping. The interferometer analyzer performs these types of operations automatically.

Example of the fringe scan method: Four images loaded for each π/2

An example of measurementusing the fringe scan method:
Analysis result obtained by calculating phases from the four fringe scanned images, and by phase unwrapping (bird’s eye view)

An interference fringe analyzer using the fringe scan method (Fringe Analysis System A1)

Example: Measurement of a Transmitted Wavefront

This figure shows an optical system for measuring the transmitted wavefront of an optical pickup object lens, using a Fizeau interferometer. The optical pickup object lens is a double-sided aspherical lens with excellent aberration correction properties. When plane waves (or spherical waves) enter, spherical waves with an extremely low degree of aberration are emitted. Therefore, when an infinite lens is used, plane waves emitted from the interferometer enter the test lens, and the beam passing through the lens returns at the reference spherical surface, permitting measurement of the transmitted wavefront aberration.

 

When a finite lens is measured, parallel rays emitted from the interferometer enter the test lens. Due to the effect of the collimator lens, they enter the test lens, transforming from convergent to divergent light. The transmitted beam likewise returns at the reference spherical surface, permitting measurement of the transmitted wavefront aberration. When a finite lens is measured, it is necessary to ensure that the focal point of the collimator lens and the object point of the test lens are in conformity, so special jig with a built-in collimator lens is required.

Measurement of the Transmitted Wavefront of a Lens

The figure shows an example of an analysis of a transmitted wavefront of an optical pickup object lens, using the FI251N interferometer and the Fringe Analyzer A1. When measuring the transmitted wavefront of a lens, third-order aberrations are important considerations. This analyzer calculates the amounts of the P-V and RMS values of the entire surface of the wavefront, as well as third-order aberrations (tilt, defocus, astigmatism, coma aberration, and spherical aberration). The window on the right displays third-order aberrations. Here, tilt and defocus are problems caused by the interferometer – lens – reference spherical surface alignment, which is not a very important issue. In lens inspections, the three aberrations—astigmatism, coma aberration, and spherical aberration—are major problems, and investigations of the amounts and directions are very important.

Summary

Interferometers can measure surfaces of glass, metal, plastic, ceramic and other materials (whether the surfaces are flat, spherical, cylindrical, quadric two-dimensionally curved, or aspherical), provided the surfaces are polished. It can also easily measure transmitted wavefronts of lenses. This is why interferometers play important roles in the optical industry and other fields.

 

Applications

  • Measurement of the shapes of a wide variety of surfaces and transmitted wavefronts including glass and plastic lenses for optical recording systems (camera lenses, copier lenses, optical pickup object lenses, etc. and optical communications, etc.). Also, measurement of shapes of transmitted wavefront.
  • Measurement of the shapes or transmitted wavefronts of flat plate surfaces of mirrors, filters, prisms, LCD glass, glass discs, glass components for optical recording systems, corner cube reflectors, hologram elements, etc.
  • Measurement of the shapes of a wide variety of mechanical parts (metal or ceramic seal part surfaces, blades, gears, ball bearing surfaces, etc.), and electric/electronic components.