I will use an high cri led lamps(95 Ra models also available). You should take in consideration also problem of directionality of the light, the leds are generaly more directional than a filament lamps.

You can also make amber Led (mono chromatic) whch will give you better focused image. the best would be to have a 3 color led (RGB) and make 3 pictures

None of the commonly available LED sources do a very good job approximating the spectral radiance exitance of a incandescent filament lamp.  CRI is a test of how close the color of a set of moderate chroma painted papers appear compared to some standard conditions (either natural daylight or an incandescent lamp).  You can place the lamp into a fixture along with the incandescent lamp and you will often see that the lights are not visually identical.  One classic issue which may impact your use is that the LED white is generally deficient in red energy while the incandescent is quite rich.  Thus natural objects with a  violet, deep red or magenta appearance will appear as blue, dark gray or dark cyan under a standard LED.  Thus I agree with the recommendation to avoid the Blue+Yellow phosphor lamps and go with a 3 or 4 LED lamp.

Silvio, Jean-Mark, Danny, thank you for your answers! I should have specified that there is no need to get the exact same spectrum of the lamp from the LED source, I just need it to be rather wide, covering .4 - .9 um range with no strongly marked gaps and peaks in it. As smooth as possible. It is not meant for visual study, the task is more spectroscopic, and hence, the spectrum of the sample I get at the output will be normalized by the spectrum of the illuminating source. And later the colors will be calculated digitally in respect to CIE. The problem is to get a LED with a united  monolayer emitting surface, so that its image after condenser would appear continuous. And it also should have a high luminosity (not the integral power , but luminosity). And the emitter size is better to be as small as possible, to have a high spatial coherence. Supercontinuum is the best option and I use one, but those are expensive and I am looking for an analogue among LEDs. I added a link on a youtube vid clearing out the idea.

https://www.youtube.com/watch?v=RTM01tovWlo

http://www.youtube.com/watch?v=eFIGgJ0anl0

If you really need to have near IR up to 900 nm, then no single white LED will cover that. You will then need to combine the light from e.g. a white LED with an IR LED into the same location and direction range, and that will require collimation, dichroic filters, and re-imaging, similar to the RGB LED light engines of commercial LED video projectors.

You say you need high "luminosity"; in my terminology that would be high radiance. The highest white LED radiance available is that of automotive headlamp LEDs, like the OSRAM OSTAR Headlamp, or comparable products from other vendors. (Note that headlamp (and/or projection) LEDs have no silicone lens; the chips are in air. It is an often overlooked fact that while the silicone lens increases flux, it decreases radiance). These LEDs come in 1 mm² packages and larger, so a 1 mm² emitting area is the smallest you can get, and this should be larger than what your optical system can accommodate. So you will have to throw away light anyway.

To achieve homogeneous irradiance on your sample, I would recommend to use (a) such an LED. Use (b) an off the shelf aspheric condensor lens for collimation. (c) Add a circular baffle of a proper diameter (see below) to cut away the light you don't need. (d) Use the condensor system of your microscope to image the circular baffle onto your sample; adjust the baffle diameter to match your field of view. This is the standard Kohler illumination approach, which will work well in your case. You will make use of the fact that these LEDs are inhomogeneous in location (phosphor grains, current spreaders etc) but homogeneous in direction, at least up to, say, 45 deg from the optical axis. This homogeneity in direction is transferred by the initial condenser lens to the baffle plane.

You can start with the single LED approach. If you find you need more spectral width, you can replace your simple LED + condensor lens light engine with the more complicated dichroic filter approach; as long as your light engine emits are narrow angular beam with homogeneous irradiance in the central part of the cross section, that should work.

However: Why do you want to replace the halogen lamp in the first place? It's a great broad band source.