Focusing

Abstract

We present solutions to two problems arising in the context of automatically focusing a general-purpose servo-controlled video camera on manually selected targets: (i) how to best determine the focus motor position providing the sharpest focus on an object point at an unknown distance; and (ii) how to compute the distance to a sharply focused object point.We decompose the first problem into two parts: how to measure the sharpness of focus with a criterion function, and how to optimally locate the mode of the criterion function. After analyzing defocus as an attenuation of high spatial-frequencies and reviewing and experimentally comparing a number of possihie criterion functions, we find that a method based on maximizing the magnitude of the intensity gradient proves superior to the others in being unimodal, monotonic about the mode, and robust in the presence of noise. We employ the Fibonacci search technique to optimally locate the mode of the criterion function.We solve the second problem by application of the thick-lens law. We can compute the distance to objects lying between 1 and 3 m with a precision of 2.5 percent, commensurate to the depth of field of the lens. The precision decreases quadratically with increasing object distance, but this effect is insignificant at the (small) object distances investigated.The solutions are computed in the time required to digitize and filter 11 images, a total of approximately 15 seconds per point for this implementation.

A Bayes-spectral-entropy-based measure of camera focus using a discrete cosine transform

“…In a typical image the intensity varies slowly from point to point across the image, which means that its spectrum obtained with the DCT is dominated by the coefficients of lower orders. It is well known that the DCT is closely related to the discrete Fourier transform (DFT), which is a standard tool in signal analysis and has previously been reported by authors like Krotkov (1987), Gillespie et al (1989) and Chern et al (2001) as the preferred transform for spectral-based focusing algorithms. However, the DCT has a greater energy-compaction property than the DFT, meaning that most of the image information tends to be concentrated in a few low-frequency DCT coefficients, approaching the Karhunen-Loève transform (which is the optimum in the decorrelation sense) for signals based on certain limits of Markov processes.…”

“…And since the DFT's basis functions are complex, this entails a larger computational load than when using the DCT. Furthermore, Krotkov (1987) and Yeo et al (1993) suggest that the spectrum of the DFT contains some information that is superfluous to the task of focusing (e.g., the phase information). Based on these arguments, we chose the DCT to be the basis of our focus measure in preference to the DFT.…”

“…Passive focusing based on image quality is a common tool in general-purpose CCD cameras and consists of three major parts: the region being focused (the focusing window); a measure of focus, which yields a maximum at the focused position; and an optimization algorithm, which searches for a global maximum of the focus measure. Many types of focus measure have been investigated in microscopy (Firestone et al, 1991;Yeo et al, 1993;Santos et al, 1997;Geusebroek et al, 2000), digital holography (Gillespie et al, 1989) and digital photography (Krotkov, 1987;Subbarao and Tyan, 1998;Widjaja and Jutamulia, 1998;Choi et al, 1999;Chern et al, 2001;Lin et al, 2004;Yap and Raveendran, 2004). Usually, these measures are calculated using certain norms of the image gradients or derivatives (Krotkov, 1987;Subbarao and Tyan, 1998;Chern et al, 2001), manipulation of gray level histograms (Krotkov, 1987;Chern et al, 2001) or operations on the longest lines in the images (Lin et al, 2004).…”

Design and implementation of algorithms for focus automation in digital imaging time‐lapse microscopy

“…The fitting search represented in Figure 2A used the parameters [5,10], i.e., it sampled at z ϭ Ϫ20, Ϫ10, 0, 10, 20, where 0 denotes its starting position. It performed well even on noisy data, such that it would probably be judged to be in focus while tracking subjects moving at a rate of up to one step per evaluation; it crossed the five-step discriminability threshold at approximately 0.5 steps per evaluation.…”

“…There is a good deal of literature on the subject of autofocus for microscopy and robotics in general (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15). Fitted with a video or digital camera and a motorized stage under computer control, the typical autofocus microscope system uses two complementary algorithms to achieve focus.…”