This is a 5 years old case, but something can still be added.
At first a bad joke that has waited 5 years to be written:
If one searches the web marketplaces for carved copper plates he soon founds that many of them, especially those which contain fine drawings, are made for printing. Some ink is still visible in the grooves because the grooves would not stand powerful cleaning. The accepted answer seemingly covers this fact, but I would still make one minor change:
Some actual info.
Now it's a little too late ask for a real photo of your real engraving. It would have been useful as a goal what should be predicted by starting from an image of untouched metal plate and your line drawing. I must make some guesses. The first guess is that you want glossy, like manually engraved grooves (see NOTE1) and the result should present them with good contrast, but still as copper. Dirty looking black shadows nor pure white glosses (due the limitations of RGB color system) are not wanted. The result should be like the lights were set with photographer's best effort.
Here's some grooves on a plate which reflects like polished metal and is colored to reddish brown. They are drawn in a 3D CAD program - only a simple one, nothing ultra complex stuff like Maya or Blender. But but at least it shows what can easily be got in a computer when screen resolution is enough and less than photorealistic rendering can be accepted:
The vieving direction and the rotating position of the plate are selected so that the quite large bright light source doesn't make straight on the face reflections on the untouched surface, but grooves have as much gloss as possible. I guess you expect the same.
The grooves are equally wide, but V- and U-profile grooves look wider. That's because the flat bottom grooves cannot be glossy if the untouched surface must not have glossy areas. I guess your grooves are something between the V and U.
Your drawing is quite dense when compared to its resolution. Our copy is also blurry and full of JPG noise. I guess you have a non-blurry noiseless PNG version, but there's many only 3 px wide gaps in your drawing and your black bitmap line is 1 px wide. We can decide that we cannot make especially high resolution shadings to the grooves which we generate from your drawing. The max line width can be only 3 px. Transparency at the line edges fortunately give a little more playground.
My grooves are 15 px wide in the rendered image. If we scale it down we can see that 2..3 px wide lines still can be (with a little imagination) considered to have some depth:
So it's useful to try to generate a shaded groove from your 1 px wide line.
As said, our copy of your drawing is blurry and full of JPG noise. Many close lines have melted together and look wide grey blur. Showing the method with our copy of your drawing is not plausible.
I made my own rudimentary line drawing in illustrator with 1 px line width and pasted it to Photoshop. It's distorted to fit the perspective of your copper plate photo:
Zoom in shows that lines are no more 1 px wide. Anti-aliasing has made lines blurry. It resembles what we can see in your drawing.
It's not originally drawn as pixel perfect and distorting it for the perspective increased the blur. If possible, one shouldn't scale nor distort bitmap images which have this dense details. But fortunately there's no noise.
We do not use layer style Bevel&Emboss nor filter Stylize > Emboss to generate the shading. They are said several times in other answers, so we try something else.
Make a duplicate of the drawing layer and adjust its color to full white with the curves.
Move the white layer content 1px downwards and 1 px to left:
Move the copper plate layer on the top and give to it blending mode =Color:
There's too much black and full white. Antialiasing transparency generates some intermediate shades. You can balance these colors by inserting a curves layer. Reduce full black and white and increase the amount of light copper:
It maybe isn't a good idea to take any color to the drawing from the copper plate photo, because it's also a noisy image. In theory the engraved lines are pure copper and thus earn own pure colors. That can be got by placing the line layers on top with blending mode =Normal and adjusting the bright and dark color to resemble copper.
Anti-alias transparency creates a good amount of intermediate colors also in this case, but to keep it bright enough reduce the opacity of the dark layer.
In this case the difference isn't dramatic between this and the previous method:
It's easy to think that in Illustrator or other vector drawing program you use the simple "2 separate drawings" method without blur, everything will be razor sharp. Envelope distortions can be used to fit the shapes and texts with a single click into the perspective of your copper plate photo with zero extra blur:
But the computer renders it to raster image to display it. The result is a little sharper, but not radically different than the bitmap version:
A zoom in view of the screenshot above reveals it's full of blur caused by antialiasing:
Placing your drawing as a fake engraving onto your copper plate starts by scaling the plate image bigger so that there's no reason to make the drawing smaller. Its 1 px line width cannot be squeezed, the only result would be blur:
The next step is to lift the contrast with curves. Some intermediate greys are needed to keep the image together:
The white should be converted to transparency. One way to do it is to use the negated image as its own layer mask. But as well you can select color range, pick the white and insert some fuzziness:
Pressing DEL removes white and most greys:
Make a duplicate layer and apply Image > Adjust > Invert to get a bright version. Move it 1 px downwards and 1 px to the left:
Move the copper plate layer to top and give to it blending mode =Color. Insert a curves layer above the line drawings to adjust the darkness and brightness of the parts of the lines:
You want to distort the drawing to the right perspective. Link its layers in the layers panel, goto Edit > Transform > Distort and drag the corners. This generates new anti-alias blur and you must to readjust the curve:
The shading of the groove isn't well visible when the image is zoomed out. If you close the dark layer you get some light boost. It can look attractive because you get more light without making the groove white. But if someone zooms in he sees there's no shading, the image looks painted on the plate with a light color.
NOTE1: The preceding story assumed clean grooves. There's also another style to make engravings. One can use "burring tools" which rotate or do high frequency chiseling. They make highly non-uniform groove bottoms and create powder-like gloss effect:
This "burred" groove simulation takes its color from the copper plate photo like above, but the lines are simply masked black and white noise. It contains randomly pixels between black and white. It can be made by inserting 100% monochrome noise to solid 50% grey layer. Here's the line pattern with noise:
The extras can be removed by inserting the line pattern as white on black to the layer mask or by making a selection and deleting.
The unfortunate fact is that the line cannot be as narrow as with clean grooves. If there's less than 4 px wide noise lines they easily start to look disintegrating, because random blacks or nearly blacks have a good possibility to make wide enough clusters.