· · · · b λ = 532GLYPH<.notdef>nm a λ =GLYPH<.notdef>612GLYPH<.notdef>nm c λ = 612GLYPH<.notdef>nm d λ = 532GLYPH<.notdef>nm Fig. 3. The measured radial intensity profile of the gener- ated spot (stars) and the speckle correlation functions of the illumination (NA = 0 . 95, triangles) and the imaging (NA = 1 . 49, dots) microscope objectives. Fig. 2. Fluorescence (a, c) and excitation (b, d) images taken at the position of a probe sphere hidden under a layer of zinc oxide. The probe sphere has a radius of R = 150 nm. The images are taken at the back of the sample where the sphere is directly visible. In (a) and (b) we focus a plane wave onto the sample. Scattering creates a random specular pattern of excitation light re- sulting in a small amount of fluorescent response of the probe sphere. In (c) and (d) we illuminate the sample with a shaped wave which is created to maximize the fluorescent emission. Aside from the fluorescent emission enhancement we see a sharp focus of excitation light. All intensities are in counts/second. the excitation light (b). Nothing in the speckle pattern reveals the position of the probe. If a shaped wave, cre- ated to maximize the fluorescent emission, is focussed onto the sample we measure an intensity enhancement of the emission (c) and we see a sharp focus of excitation light at the position of the probe (d). It is surprising to see that this focus is smaller than the probe sphere. The radial intensity profile in the focus is shown in Fig. 3 together with the speckle correlation functions (SCFs) measured through both the illumination and the imaging microscope objective. The SCF is equal to the point spread function (PSF) of an optical system [16–18] giving the resolution limit of the illumination and imag- ing optics. The measured intensity profile has a half width at half max (HWHM) of 111 ± 5 nm and a peak in- tensity of 32 . 1 times the average speckle background in- tensity. The size of the created spot is not limited by the illumination system, as it is substantially smaller than the measured illumination SCF. We also see that the measured size of the created spot is equal to the SCF of the imaging system, meaning that the created spot is smaller than or equal to the resolution limit of our microscope objective. From literature we know that linear polarized light can be optimally concentrated to an elliptical focus. [19] The HWHM of the two axis of this elliptical focus are given by 0 . 28 λ/n$_{eff}$ and 0 . 17 λ/n$_{eff}$ and the focal area by 0 . 048 πλ $^{2}$/n2 $_{eff}$. In our experiment this would result in a smallest possible focal area of 0 . 02 µ m 2 with the HWHM of the two axes 110 nm and 67 nm. The resolution of our imaging microscope objective does not allow us to resolve the short axis of the spot. However, we see that without explicitly minimizing the spot size, the created spot area does not exceed the smallest spot area physically possible by more than 68%. To further investigate the created focus, we compare the intensity enhancements of the emission η em and exci- tation η $^{ex}$. For the excitation intensity, the enhancement 2 In Fig. 2 we see a typical result of the experiment. When we illuminate the sample with a focussed plane wave, we measure a low fluorescence response from a R = 150 nm probe (a) and we see a speckle pattern in Using a wave front synthesizer, similar to the one dis- cussed in Ref. [9], we spatially divide a monochromatic laser beam ( λ = 532 nm) into up to 640 square segments of which we individually control the phase. The shaped beam is focussed onto our sample using a microscope objective (NA = 0 . 95). The same microscope objective is used to capture the fluorescence from a probe hidden under the scattering layer. At the back of the sample we use an oil-immersion microscope objective (NA = 1 . 49) to directly image the excitation and emission light at the probe. A digital feedback system that monitors the amount of fluorescence, tailors the wave front to max- imize the emission of a probe sphere hidden under the scattering layer. Both the fluorescence measured at the front and at the back of the sample were used indepen- dently to feed the digital feedback system and we did not observe a difference in our results. Because detect- ing fluorescence at the back of our sample allows us to use low shutter times on our camera, we used this signal as a feedback for most of our measurements. range between 7 . 5 ± 1 µ m and 25 ± 4 µ m and have a mean free path of ℓ = 0 . 7 ± 0 . 2 µ m. By measuring the angular resolved transmission through the ZnO layers [13], we determined their effective refractive index n$_{eff}$ to be 1 . 35 ± 0 . 15. [14,15]