Determination of thin hydrodynamic lubricating film thickness using dichromatic interferometry L. Guo,1 P. L. Wong,1,* F. Guo,2 and H. C. Liu2 1

Department of Mechanical and Bio-medical Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China


School of Mechanical Engineering, Qingdao Technological University, 11 Fushun Road, Qingdao 266033, China *Corresponding author: [email protected] Received 18 April 2014; revised 7 August 2014; accepted 7 August 2014; posted 7 August 2014 (Doc. ID 210255); published 10 September 2014

This paper introduces the application of dichromatic interferometry for the study of hydrodynamic lubrication. In conventional methods, two beams with different colors are projected consecutively on a static object. By contrast, the current method deals with hydrodynamic lubricated contacts under running conditions and two lasers with different colors are projected simultaneously to form interference images. Dichromatic interferometry incorporates the advantages of monochromatic and chromatic interferometry, which are widely used in lubrication research. This new approach was evaluated statically and dynamically by measuring the inclination of static wedge films and the thickness of the hydrodynamic lubricating film under running conditions, respectively. Results show that dichromatic interferometry can facilitate real-time determination of lubricating film thickness and is well suited for the study of transient or dynamic lubricating problems. © 2014 Optical Society of America OCIS codes: (120.3180) Interferometry; (120.4820) Optical systems; (240.0310) Thin films.

1. Introduction

Optical interferometry has been widely used for measuring film thickness in lubrication. Its concept is illustrated with an optical lubrication system in Fig. 1. A lubrication film is bound between a steel surface and a chromium-coated glass disk. A light beam is projected onto the contact through the glass disk. The resultant interferogram is formed by the interference of the first two major reflections and with others of higher order. Gohar and Cameron [1,2] were the first to utilize optical interferometry successfully in the research of lubrication. They presented the first ever optical interferogram of a typical elastohydrodynamic lubricated (EHL) contact with a unique horseshoe-shaped film. Their experimental setup used the concept shown in Fig. 1, except 1559-128X/14/266066-07$15.00/0 © 2014 Optical Society of America 6066

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that the slider was replaced by a steel ball. A major limitation of the optical technique is its requirement that one or both surfaces be transparent, which differs from the case in typical real engineering steel-on-steel contact. However, optical interferometry provides far more detailed information on the shape of lubricating films compared with other methods such as x ray and ultrasound, which provide only the average film thickness. Hence, optical interferometry has become the most widely used technique in experimental EHL research since its applicability to lubrication studies was proven by Cameron and his group at Imperial College in the 1960s. In the early work of Foord et al. [3], different light sources, including monochromatic, dichromatic (use of two beams of different wavelengths), and chromatic (white light) were evaluated. Monochromatic interferometry can measure a very thick film (readily up to a few microns using a laser and theoretically to several tens of microns if systems with high optical

Fig. 1. Schematic illustration of an optical lubrication system.

quality are used). Chromatic interferometry provides higher resolution than monochromatic interferometry but a shorter measuring range of up to about 1 μm. Dichromatic interferometry combines the advantages of these two former methods. In the optical EHL work of Cameron and coworkers [1–3], a monochromatic light source was mostly used. Dark interference fringes were used to calculate film thickness because of their high definition. The magnitude of optical film thickness at the location of dark fringes is equal to a multiple of half the wavelength of the light source. Hence, the minimum measurable film thickness is restricted to the interference fringe of the first order. The fringe intensity method, which uses the intensity of interference to calculate the film thickness, was proposed by Roberts and Tabor in the 1970s [4]. The intensity method significantly enlarges the resolution of an interferometry measurement. For a simple interference system with only the two major reflections as shown in Fig. 1, the variation in interference intensity with film thickness (I-h) follows a cosine function. However, in a conventional optical EHL setup, the variation in interference intensity with film thickness deviates from the ideal cosine form because of the complex optical properties of the Cr layer and steel surface, as well as the effect of multireflections. The intensity method was also adopted by Luo et al. [5] in the 1990s. They carefully tuned the optical test rig to acquire a cosine variation of intensity with film thickness. Subsequently, Guo and Wong [6,7] completed a full analysis of the optical characteristics of a conventional optical EHL setup with multibeam interference. The complex optical properties of all materials involved and the multibeam reflectance of the system were evaluated. At the end of their study, the intensity variation with film thickness was mathematically modeled. Therefore, film thickness can be directly interpreted from interference intensities and is not restricted to the points of dark fringes. Optical interferometry has recently been applied to the study of hydrodynamic lubrication by the present authors. An optical test rig was developed to measure the hydrodynamic lubricating film thickness in a slider-on-disk contact [8]. A schematic illustration of this test rig is shown in Fig. 2. The key measuring parameters of the sliding tester include

Fig. 2. Schematic illustration of the present setup using dichromatic interferometry measurement.

the lubricating film thickness and friction force. Considering the magnitude of a typical hydrodynamic lubricating film thickness, a monochromatic light source is adopted. Film thickness can be extracted from any of the interferograms of the lubricated contact only if the fringe orders are known. The fringe order can be obtained by tracing the intensity changes at a selected arbitrary spot in the interference image of the contact during the increase or decrease of the lubricating film thickness in the acceleration or deceleration processes, respectively. However, following an exact spot requires an extremely stable slider contact, which is unachievable when the slider is connected to a load cell for friction measurement. During the acceleration or deceleration processes, the contact area shifts because tension changes from the connecting wire to the load cell. Furthermore, determining changes in the fringe order by stopping the running disk cannot be implemented when investigating dynamic or transient lubrication behaviors, such as rapid changes in the film thickness caused by shock. Furthermore, intensity data may be lost during measurement if the lubricant film is rapidly formed and the varying intensity rate exceeds the sampling rate of image acquisition. Thus, film thickness must be directly measured from a single interferogram of the contact without stopping the test. Dichromatic interferometry using two light sources with different colors (two wavelengths) is widely used in applied optics to evaluate aspheric surfaces for the wide range of sensitivities of the technique [9–12]. In a typical setup, two lasers are used successively to form interferograms with the same area of interest. Wyant [12] showed that by combining the two interferograms formed by lasers of different wavelengths, the resultant interferogram can be taken as the result of using a pseudolight source with longer wavelength. This method was mainly developed for static measurements, 10 September 2014 / Vol. 53, No. 26 / APPLIED OPTICS


i.e., component interferograms are obtained successively with different lasers. The concept of two-wavelength interferometry was extended by Polhemus [13] to real-time dynamic testing by simultaneously operating two sources with different wavelengths. The measuring range of two-wavelength interferometry was further enhanced from one or two microns to a few tens of microns by phaseshifting [14], improving data analyses [15,16], and, more recently, signal processing based on arithmetic properties [17]. This paper presents our recent development of the dichromatic interferometry technique for measuring hydrodynamic lubricating film thickness, especially for directly determining the film thickness under running conditions. The typical thickness of the thin film hydrodynamic lubrication regime is approximately two microns. Hence, the original twowavelength interferometry proposed by Wyant [12] is adopted in the current study without implementing complex data processing or analysis algorithms. 2. Principle of Dichromatic Interferometry

Methods for conventional optical measurement of lubricating film thickness are based on the periodic characteristics of the relationship between the interference intensity I and film thickness h. The relationship is a cosine function if the interference is formed by the two major reflections [5], as illustrated in Fig. 1, or a skewed cosine curve if all reflectances are considered (referred to as multibeam intensity interference in [6]). The difference in film thickness between the two points with the same intensity and phase can be expressed as Δh  ΔN ·

λ ; 2n


where h is the film thickness, N is the fringe order, n is the refractive index of the lubricant, and λ is the wavelength of the light. When considering only one period as ΔN  1, the cycle of the interference intensity variation with film thickness is T

λ : 2n


The two beams with different colors (λ1 and λ2 ) simultaneously form interference images. Superimposing the two intensity curves against the film thickness, i.e., (I 1 − I 2 ) versus h, along the same line of measurement provides a resultant periodic curve with an envelope cycle (see Appendix A), Te 

λ1 λ2 ; 2njλ1 − λ2 j

λ1 λ2 : jλ1 − λ2 j


Obviously, the cycle of the envelope is much greater than that of I versus h from a light beam of a single color. The film thickness in the first cycle of the intensity and film thickness variation (within the first-fringe order, N  1) can be deduced directly from the measured intensity. Hence, a longer wavelength results in a broader range for film thickness measurements. Thus, dichromatic interferometry has a broader measuring range because of its long equivalent wavelength of the envelope. The technique is used mainly because of the slower moving rate of the envelope corresponding to the change in film thickness compared with that of fringes with monochromatic interference. The ratio between the two moving rates is equal to (Appendix B) venvelope jλ1 − λ2 j  : vλ1 λ2


Therefore, the order of the envelope cycle can be easily identified. For example, if λ2 is 638 nm (red) and λ1 is 532 nm (green), the speed ratio is 0.199. Hence, the envelope cycle moves approximately one-fifth slower. 3. Experiments

All experiments were carried out using our selfdeveloped fixed-incline slider test rig [8]. A schematic of the process of film thickness measurement and the new technique are shown in Fig. 2. The sliding contact is constructed with a rotating glass disk and a stationary slider, in which the inclination angle can be fixed and adjusted using eight adjustment bolts located on the load arm. The surface of the glass disk is partially coated with a Cr layer of 20 nm in thickness for partial reflection, and a transparent SiO2 layer of about 200 nm is added on top for protection. The film thickness at the exit was measured in the tests. The change in film thickness at any location on the slider surface is equal to the change in film thickness at the exit when a slider with fixed inclination stops. Lasers of green and red colors (wavelength 532 and 638 nm, respectively) were selected as light sources. A three-CCD camera with higher accuracy than a colored-CCD camera was used to obtain the interference intensity using a Bayer array. The roughness of the steel slider was 11.8 nm, and its length and width were 4 and 9 mm, respectively. PAO400/40 was used as the lubricant, the properties of which are listed in Table 1. The tests were carried out in a controlled


where T e is the envelope cycle. The envelope is equivalent to the curve of intensity and film thickness variation of a longer wavelength λe [12], 6068


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Table 1.

Properties of PAO400/40 Used in the Tests

Viscosity (mPa s) at 21°C 879.8

Refractive Index 1.47

Summation Subtraction

Fig. 3. Interferogram used as the standard (YF, yellow fringe).

environment (ambient temperature 21°C  1°C, humidity 33%  1%). To implement the new technique, a dichromatic interference image with known film thickness variation is needed as a standard. A standard image was captured using a wedge gap with a fixed inclination. The steel slider was tilted and rested on the glass disk. The wedge gap was filled with the lubricant PAO400/40. The lower edge of the slider was in contact with the glass disk surface, i.e., zero film thickness. The selected standard image is shown in Fig. 3. The intensity variation of the two different color beams (red and green) along a line (as highlighted in Fig. 3) was normalized to their adjacent local maximum and minimum intensities. The difference of the two normalized intensity curves (I red − I green ) is plotted in Fig. 4. The total number of pixels for the full length of the slider (4 mm) was counted to be 751. The magnification of the image was thus 5.326 μm∕pixel. The inclined angle of the slider can be readily obtained from the interferogram of the red or green beam. From the interferogram of the green beam (λ  532 nm), the cycle was measured to be 50.67 pixels on average (or 269.87 μm in length). Hence, the inclination was calculated to be 6.705 × 10−4 rad. The envelope of the normalized intensity difference curve was obtained using a Hilbert transform [18], as shown in Fig. 4. The envelope obtained using a Hilbert transform was not smooth, but provided the location of the first and second valleys, which is important for automatizing the measurement process in subsequent development. The curves of summation and subtraction of the two intensities, (I 1  I 2 ) and (I 1 − I 2 ), are plotted in Fig. 5. The two valleys of the curve of (I 1 − I 2 ) were

Intensity difference








400 Pixel



Fig. 4. Analysis results of the standard interferogram.

Normalized intensity








400 Pixel



Fig. 5. Variation of summation (I 1  I 2 ) and subtraction (I 1 − I 2 ) of intensities.

Table 2.

Calibrated Film Thickness of the Yellow Fringes

Yellow Fringe Order 1st 2nd

Film Thickness (nm) 810.6 1889.1

represented by the 227th and 529th pixels. These valleys correspond to the locations of the maximum intensities of (I 1  I 2 ), which are the bright yellow fringes shown in Fig. 3. The bright yellow fringe is the result of the sum of the constructive interferences of the two primary colors. Hence, the film thicknesses of the first and second yellow fringes can be deduced from the known angle of inclination and are listed in Table 2 as a reference. Thus, the cycle of the envelope was determined as 1078.5 nm. The effectiveness of the dichromatic interferometry for measuring lubricating film thickness was evaluated under static and running conditions, and the results were compared with those obtained using conventional monochromatic interferometry. 4. Results and Discussion

Dichromatic interferometry was applied to measure the inclination of static wedge gaps and demonstrate the reliability of the current technique. Considering that monochromatic interferometry can provide accurate results, the inclinations obtained using the new technique were compared with those obtained using monochromatic interferometry. Dichromatic interference images with different inclinations under conditions similar to those of the standard image were captured and analyzed, as shown in Fig. 6. The location of the first yellow fringe was detected. Given the film thickness represented by the first yellow fringe provided in Table 2, the angle of inclination was then calculated. The calculated inclinations were compared with the results detected using monochromatic interferometry and are shown in Table 3. The table shows that the inclinations obtained through monochromatic interferometry for cases #1 and #2 are 5.381 × 10−4 and 4.208 × 10−4 rad, respectively. The inclinations calculated using dichromatic 10 September 2014 / Vol. 53, No. 26 / APPLIED OPTICS


3.0 Intensity difference

Intensity difference

3.0 1.5 0.0 -1.5 -3.0 0


400 Pixel



(a) Angle I

1.5 0.0 -1.5 -3.0 0


400 Pixel



(b) Angle II

Fig. 6. Interferogram and analysis results of the static slider contact with different inclinations (the arrow indicates the yellow fringes). (a) Angle I. (b) Angle II.

Table 3.

Cases #1 #2

Inclined Angle Measurement Using Dichromatic and Monochromatic Interferometry

Angle of Inclination (×10−4 rad)

Pixel Number of First-Order Yellow Fringe



283 362

5.378 4.205

5.381 4.208

(aa) 0.25 mm/s

(bb) 0.5 mm/ss


interferometry were 5.378 × and 4.205 × 10−4 rad. Differences between the two measured results are lower than 0.1%. Thus, the accuracy of dichromatic interferometry fulfills requirements for film thickness measurement. Dichromatic interferometry was applied to determine the film thickness under a running lubricating slider contact. During dynamic film thickness measurement, a constant inclined angle of the slider (1:2064) was adopted and the film thickness was measured under different speeds. Each measurement was repeated three times. Monochromatic measurement was also performed, and the results obtained using the two techniques were compared. Figure 7 shows the dichromatic interference images formed under different speeds with a constant load of 10 N. Changes in position of the second-order wide yellow fringe with different speeds are shown. Figure 8 shows a log–log graph of the film thickness against speed. The film thickness was calculated using the two techniques. Generally, the two curves coincided, especially under low speeds. All data points which are the average of three separate measurements are shown with uncertainties in Table 4. The maximum difference in the film thickness for the specified speed range using the two methods was approximately 40 nm at a speed of 2 mm∕s. This finding indicates that the maximum relative error 6070

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(cc) 1.0 mm/ss

(dd) 1.5 mm/ss

(e) 2.0 mm/ss

Fig. 7. Interference images under different speeds (positions marked represent the second yellow fringe). (a) 0.25 mm∕s, (b) 0.5 mm∕s, (c) 1.0 mm∕s, (d) 1.5 mm∕s, and (e) 2.0 mm∕s.

(or accuracy) for dichromatic interference is lower than 2.5%, as shown in Table 4. The error can be attributed to the fluctuation of the disk during the tests, particularly at high speeds. The repeatability

Film thickness (um)

2.0 1.5


Monochromatic Dichromatic 0.5

0.5 1.0 Speed (mm/s)


2.0 2.5

Fig. 8. Changes in film thickness with speed.

of the experiments was very good as reflected by the small uncertainty of each measured point listed in Table 4. Monochromatic interferometry requires stopping the experiment to monitor the drop of the slider and measure the film thickness. By contrast, dichromatic interference requires only one interference image of the lubricant film to calculate the film thickness. Therefore, dynamic measurements without the need to stop the disk are realized. The envelope was formed by combining the two interference fringes to provide an equivalent intensity and film thickness variation in a larger cycle. Equation (3) indicates that the cycle of the envelope is related to the wavelength of the two beams. The large product of the two wavelengths or their small difference results in a larger envelope cycle. Wyant [12] theoretically obtained an equivalent wavelength of 28.5 μm using dichromatic light beams with wavelengths of 496.5 and 488 nm. Real-time measurement of the thickness of the hydrodynamic lubricating film requires the two interferograms formed by two beams to be simultaneously obtained. Therefore, the selected wavelengths must correspond to the response spectrum of the camera used, which limits the envelope cycle. In the current experiment, lasers with wavelengths of 532 and 638 nm were used. The theoretical envelope cycle was 1.089 μm based on Eq. (3). This result is correlated with the measured cycle of 1.079 μm. However, the lasers can be optimized to obtain an envelope with a larger cycle. For example, lasers with wavelengths of 550 and 600 nm may be Table 4.

Film Thickness Measurements Using Monochromatic and Dichromatic Interferometry

Film Thickness (nm) Speed (mm/s) 0.25 0.50 1.00 1.50 2.00



Accuracy (%)

556.723.5 −29.9 897.55.7 −8.9 1284.521.9 −14.5 1560.45.9 −8.7 1760.62.4 −2.5

558.440.6 −33.6 887.921.2 −21.9 1309.219.7 −23.9 1581.28.7 −10.5 1805.832.3 −35.7

0.30 1.09 1.88 1.31 2.50

selected according to the response spectrum of the camera, and the envelope cycle can be theoretically extended to 2.245 μm under similar working conditions. Dichromatic interferometry is effective for realtime determination of the film thickness, and its efficiency is higher than that of monochromatic interferometry. Counting intensity changes using monochromatic light at an arbitrary spot on the lubricated contact by intermittently interrupting the test is tedious, time consuming, and impractical for analyzing volatile or water-adsorbing lubricants, which may suffer from a significant change in viscosity during a lengthy test. For example, in the experiment described in Fig. 8, the duration of the test using dichromatic was approximately 10 min without interruption. Using monochromatic light, by contrast, causes the test to last as long as 50 min. Dichromatic interference is important for tracing the position of the yellow fringe with a known fringe order. The frame rate of the recording system was 25 fps. If the changes in the film thickness between two consecutive frames exceeds one cycle of the yellow fringes, i.e., the magnitude of the film thickness change in 1∕25 s is longer than λe ∕n, the measurement suffers from wavelength ambiguity. Measurement errors include glass disk fluctuation and stability of the wavelengths used. The bandwidths of the light sources used in the current study are 2 and 10 nm for green and red lasers, respectively. The glass disk cannot be guaranteed to be absolutely flat during dynamic measurement. Currently, the fluctuation range of the running glass disk can be controlled within 100 nm. This uncertainty will lead to slight errors in measuring the inclination and location of yellow fringes. Furthermore, the stability of the used wavelengths determines measurement error. Therefore, lasers with high stability and small bandwidth are recommended in the current measurement system. 5. Conclusions

A new optical method for measuring the film thickness of hydrodynamic lubricated contact using dichromatic interferometry has been developed. Two light beams with different wavelengths are required for simultaneous projection on the lubricating contact. Superimposing the two interference patterns results in an envelope of intensity difference and film thickness variation equivalent to an intensity and film thickness curve with a longer cycle. Using the equivalent intensity curve, the measurement range of film thickness can be enhanced compared with monochromatic interferometry. The moving rate of the equivalent intensity curve corresponding to a rapid change in film thickness was fairly slow. Hence, dichromatic interferometry can facilitate real-time determination of lubricating film thickness and is suitable for investigating transient or dynamic lubricating problems. 10 September 2014 / Vol. 53, No. 26 / APPLIED OPTICS


The change of fringe order of the envelope is

Appendix A

Suppose the two normalized intensities I 1 h and I 2 h are described by the following equations:   4nπ h  Φ1 ; I 1 h  cos λ1  I 2 h  cos


4nπ h  Φ2 : λ2



If only the positive amplitude is considered, the cycle can be expressed as T λ1 λ2 :  2 2njλ1 − λ2 j


Appendix B

Suppose the change of the film thickness is Δh in Δt seconds. The change in the fringe order of monochromatic interference is ΔT λ1 

Δh λ1 2n

2Δhn : λ1


Fig. 9. Illustration of envelope expression. 6072

2Δhnjλ1 − λ2 j : λ1 λ2




The work described in this paper was fully funded by the Research Grants Council of Hong Kong (Project No. CityU123411) and the National Natural Science Foundation of China (Project No. 51275252). The authors would also like to thank the City University of Hong Kong for providing studentship to the first author. References

Ah is the expression of the envelope, as shown in Fig. 9, and the cycle of the envelope is

T 12 

λe venvelope jλ − λ2 j Δt  ΔT  1 : λ vλ1 λ2 1



λ1 λ2 : njλ1 − λ2 j

λ1 λ2 2njλ1 −λ2 j


    2n 2n Φ1  Φ2 ; h  I 1 h − I 2 h  Ah × sin π 2 λ1 λ2 (A3)     2n 2n Φ1 − Φ2 : − h Ah  −2 sin π 2 λ1 λ2


The ratio between the two changing rates is

Combining the two equations,


ΔT λe 

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Determination of thin hydrodynamic lubricating film thickness using dichromatic interferometry.

This paper introduces the application of dichromatic interferometry for the study of hydrodynamic lubrication. In conventional methods, two beams with...
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