Dynamic point shifting with null screens using three LCDs as targets for corneal topography.

In this paper, the use of three liquid crystal displays (LCDs) as targets for an experimental corneal topographer is proposed. The main advantage is that the geometrical pattern in the target can be modified without moving any mechanical part to apply the dynamic point shifting (DyPoS) method. Some results on the capabilities of the LCDs, obtained with photo frames, for measuring a 6.37 mm radius of curvature calibration sphere, and applying the DyPoS method, are presented. It is shown that the error in measuring the radius of curvature with DyPoS is reduced to 3% of the real value and the RMS in elevation or sagitta differences is around 15 µm, 30% or 66% of the values obtained without DyPoS, respectively.

Point shifting in the optical testing of fast aspheric concave surfaces by a cylindrical screen.

A method for increasing the precision and sensitivity of the quantitative evaluation of fast aspheric surfaces through the null screen method is presented. This consists of applying small displacements to the cylindrical null screen along the optical axis. These movements allow a scan of the image spots over zones that with the analysis of a single image are more difficult to evaluate. The precision of the test is increased due to a greater density of sampling reducing the numerical errors during the integration. Results of the evaluation of an elliptical concave mirror on axis show that the numerical integration errors can be reduced from 20% for short paths to 80% for larger integration paths.

Testing fast aspheric concave surfaces with a cylindrical null screen.

A noncontact test procedure to obtain the shape of fast concave surfaces is described. A cylindrical null screen with a curved grid drawn on it in such a way that its image, which is formed by reflection on a perfect concave surface, yields a perfect square grid is proposed. The cylindrical null screen design and the surface evaluation algorithm are presented. Experimental results for the testing of an elliptical mirror of 164 mm in diameter (f/0.232) are shown.

Testing a fast off-axis parabolic mirror by using tilted null screens.

We propose the design of tilted null screens for testing off-axis segments of conic surfaces. The tilt allows us to control the size of the screen and the sensitivity of the test. For positive tilt angles the sensitivity is increased while the size of the screen is reduced in the sagittal caustic region and vice versa in the tangential caustic region. Further analysis and preliminary experimental results are presented for a fast off-axis concave parabolic mirror with an elliptical aperture. An offset distance of X(C) = 25.4 mm yields radius of curvature at the vertex R = 20.4 mm; major axis of the mirror D(M) = 49.4 mm; and minor axis D(m) = 29.5 mm.

Phase measurement for segmented optics with 1D diffraction patterns.

A simple approach for measuring the piston error between two adjacent segments in a primary mirror of a telescope, based on the one dimension analysis of the diffraction pattern produced by a divided slit, is proposed. Using two wavelengths allows an increase of the dynamic range of the measurement. The main advantages are that even maintaining the correlation based scheme used by other authors, the time of processing should be reduced. Some experimental results are presented which show that for one wavelength a precision of 3 nm and a dynamic range of 316 nm are feasible for the red line of a He-Ne laser. For the two wavelength experiments a precision of 53 nm is obtained for lambda(eq)/2 = 1670 nm dynamic range.

Null-screen testing of fast convex aspheric surfaces.

A method for null-testing fast convex aspheric optical surfaces is presented. The method consists of using a cylindrical screen with a set of lines drawn on it in such a way that its image, which is formed by reflection on a perfect surface, yields a perfect square grid. Departures from this geometry are due to imperfections of the surface, allowing one to know if the surface is close to the design shape. Tests conducted with a full hemisphere and with the parabolic surface of a lens show the feasibility of the method. Numerical simulations show that it is possible to detect surface departures as small as 5 microm.

Medium-precision null-screen testing of off-axis parabolic mirrors for segmented primary telescope optics: the large millimeter telescope.

The feasibility of using null screens for testing the segments of a parabolic segmented telescope mirror for the Large Millimeter Telescope (LMT) is analyzed. An algorithm for designing the null screen for testing the off-axis segments of conic surfaces is described. Actual screen designs for the different classes of segments of the LMT are presented. The sensitivity of the test and the required accuracies for the fabrication and positioning of the screen are analyzed. A measuring accuracy of approximately 12 microm in surface sagitta is within the reach of the technique.

Corneal shape evaluation by using laser keratopography.

Corneal topography assessment plays a fundamental role in the detection of keratoconus and the evaluation of the refractive surgery patient. The main drawbacks of the methods based on the use of Placido's disk (the most commonly used technique) have been pointed out recently, and new techniques are being sought that allow clinicians to be more confident about the measurement. Some years ago, we proposed a new technique based on a scan of the corneal surface with a low power HeNe laser beam; by measuring the deflection of the reflected beam, it is possible to compute the shape of the scanned cornea. In this paper, we explain the basic theory behind the method and present numerical simulations which show that errors in the surface heights of less than 1 microm may be obtained. In this work, we do not consider the effect of experimental errors. We discuss some possible extensions and improvements to the theory.

COVASIAM: an image analysis method that allows detection of confluent microbial colonies and colonies of various sizes for automated counting.

In this work we introduce the confluent and various sizes image analysis method (COVASIAM), an automated colony count technique that uses digital imaging technology for detection and separation of confluent microbial colonies and colonies of various sizes growing on petri dishes. The proposed method takes advantage of the optical properties of the surfaces of most microbial colonies. Colonies in the petri dish are epi-illuminated in order to direct the reflection of concentrated light coming from a halogen lamp towards an image-sensing device. In conjunction, a multilevel threshold algorithm is proposed for colony separation and counting. These procedures improved the quantification of colonies showing confluence or differences in size. We tested COVASIAM with a sample set of microorganisms that form colonies with contrasting physical properties: Saccharomyces cerevisiae, Aspergillus nidulans, Escherichia coli, Azotobacter vinelandii, Pseudomonas aeruginosa, and Rhizobium etli. These physical properties range from smooth to hairy, from bright to opaque, and from high to low convexities. COVASIAM estimated an average of 95.47% (sigma = 8.55%) of the manually counted colonies, while an automated method based on a single-threshold segmentation procedure estimated an average of 76% (sigma = 16.27) of the manually counted colonies. This method can be easily transposed to almost every image-processing analyzer since the procedures to compile it are generically standard.

Detection limits of an internal-reflection sensor for the optical beam deflection method.

The theoretical detection limit on angle deflection measurement when the quasi-critical internal-reflection method is used is calculated and compared with the more common method of using a bicell position-sensitive detector. Simple formulas for the sensitivity and resolution when the system is shot noise limited are given. It is shown that, even though the bicell detector is potentially much more sensitive for wide and well collimated beams, under typical laboratory restrictions, the internal reflection method may be more sensitive and have better resolution. It is argued that the internal-reflection method may be a tool in developing compact sensors based on the optical beam deflection method.

Polynomial fitting of interferograms with Gaussian errors on the fringe coordinates. II: Analytical study.

We consider an ideal Twyman-Green interferogram with equally spaced straight fringes parallel to the x axis and fringe coordinates that are affected by Gaussian errors. We adjust the data points by polynomial fitting to the interferograms. We use a statistical analysis to obtain analytical formulas for the expected values of the aberration coefficients. The result of the analysis shows that the expected coefficients are zero, except for tilt about x and for the comatic term, and that such deviation increases with the noise level and decreases with the number of fringes. Formulas are also obtained for the expected values of the sum of squares of the residuals. We show that the problem of choosing the wrong polynomial order is a consequence of erroneous adjustment of the data points.

Profile testing of spherical surfaces by laser deflectometry.

A method for testing the profiles of spherical surfaces is presented. It consists of measuring the transversal deflection of a reflected He-Ne laser beam when the surface is rotated around an axis located near its center of curvature. A set of formulas that enables us to calculate the shape of the profile as well as the decentering of the rotation axis is obtained. By using a simple experimental setup, we found the differences between the experimental profile with respect to the ideal one; the accuracy that was obtained is ~3 µm. The method may be improved and is useful for convex as well as for concave surfaces. With minor modifications it is possible to test large surfaces and weak aspherics.

Schlieren effect in Amici prisms.

It is shown that a system consisting of a polarizer, an Amici prism, and an analyzer may act like a phase and amplitude spatial filter capable of producing four fully distinct images. Two of these are complementary Schlieren or Foucault testlike images, another one is like a phase-edge test pattern, and the fourth is similar to a bright field image. An analysis is made of how the system works when the incident beam is collimated. The formation of the observed images can be explained by assuming that this analysis remains valid for incident beams of small covergence. Some experimental results are presented.

Comparison between toroidal and conic surfaces that best fit an off-axis conic section.

A mathematical treatment is developed to establish the difference in the sagitta between toroidal and off-axis conic surfaces. The best fit betwen these surfaces is found by optimizing the curvatures of the toroid, and a comparison is made between these results and those obtained previously.