• Each scanner component has a given rating in light-years (ly), within which radius it can detect uncloaked ships in deep space. Some scanners (known as "planet-penetrating scanners", or "penetrating scanners"/"penscans" for short) additionally have a second, lower rating, within which radius they can detect uncloaked ships in orbit of a planet, uncloaked starbases, and the statistics (owner, population, mineral concentrations, habitability values) of planets themselves. The population of Alternate Reality races' planets will always be reported as 0, no matter what it actually is. Claim Adjuster races, when viewing scan reports of a planet inhabited by a race they have set to "friend", will see the owner's habitability bars instead of their own.
  
• In addition to scanner components mounted on ships, there are a few other things that have detection capabilities:
  - Planetary scanners: inhabited planets can construct a "Planetary Scanner" from the production queue. This will use the rating(s) of the best planetary scanner component you have the tech for (it's automatically upgraded when you discover a new one).
  - AR planetary scanners: planets controlled by an Alternate Reality race cannot construct planetary scanners, but instead receive an organic scanner dependent on the population of the world. All worlds receive an ordinary scanner with a rating of (SQRT(population/10)), and worlds with an Ultra Station or Death Star starbase receive a planet-penetrating scanner with half that rating. There doesn't appear to be a cap on this formula, but very strange things happen when you put over 1 billion pop on a world.
  - SD "minefield scanning": Space Demolition races' minefields act as ordinary scanners; ships in deep space within a Space Demolition minefield will be detected by the minefield's owner as though they had been scanned.
  - PP "packet scanning": Packet Physics races' mineral packets act as scanners; packets have an ordinary and planet-penetrating rating equal to the square of the warp speed at which they are flung (e.g. a packet flung at Warp 12 will detect ships and planets within 144 ly). Packet Physics races can also detect all mineral packets and deep-space scrap in the universe.
  - IT "gate-scanning": Interstellar Traveller races' stargates act as special scanners, with a rating equal to their distance rating as a stargate. These scanners will detect planets with starbases that have stargates, and will detect the starbase as well as the statistics of the planet, but not any ships in orbit.
  - JoaT inbuilt hull-scanning: Jack of all Trades races' Scout, Frigate and Destroyer hulls have an inbuilt scanner with ordinary rating equal to (20 * Electronics tech) and planet-penetrating rating equal to (10 * Electronics tech). (The effect is based on control, not the original builder of a ship.)
  
• Multiple scanners on board a single ship (including Jack of all Trades inbuilt hull scanners) combine into a single more powerful scanner. Ordinary and planet-penetrating scanners are considered separately for this purpose. The formula is:
  
  Overall scanner rating = ((Scanner 1 rating)⁴ + (Scanner 2 rating)⁴ + (Scanner 3 rating)⁴ +...)^1/4
  
  So, if a Jack of all Trades race with Electronics tech 18 builds a Frigate with two Elephant Scanners (ordinary scanner rating 300, planet-penetrating scanner rating 200), the Frigate will have an ordinary scanning rating of (360⁴ + 300⁴ + 300⁴)^1/4 = 426 ly and a planet-penetrating scanning rating of (180⁴ + 200⁴ + 200⁴)^1/4 = 255 ly.
  
• Scanners on board multiple ships in a fleet, and scanners on a planet and on ships in orbit, do not interact. The combined scanning is simply equal to that of the most powerful scanner in each category (ordinary and planet-penetrating). So, if a ship with one Peerless Scanner (ordinary scanner rating 500, no planet-penetrating scanning) and a ship with one Elephant Scanner (ordinary scanner rating 300, planet-penetrating scanner rating 200) were in a fleet, the fleet would have 500 ly of ordinary scanning and 200 ly of planet-penetrating scanning.
  
• Scanners reveal the hull type of detected ships and starbases, and the weight of detected ships, but they do not normally reveal the complete designs unless the design is known to the scanning player (via prior combat with other ships/starbases of that design). However, War Monger races will always be able to see the designs of scanned ships and starbases.
  
• Super-Stealth races have access to additional scanners; the Chameleon Scanner is a penetrating scanner that is also a cloak (see below), the Pick Pocket Scanner is an ordinary-only scanner that allows fleets equipped with one to steal minerals from enemy ships, and the Robber Baron Scanner is a penetrating scanner that allows fleets equipped with one to steal minerals from enemy ships and planets. Detailed explanation of the special capabilities of the Pick Pocket and Robber Baron scanners is beyond the scope of this post.
  
• The lesser racial trait "No Advanced Scanners" removes most penetrating scanners from a race. Specifically, it removes:
  - The Ferret, Dolphin and Elephant scanner components,
  - The Snooper 320X and higher planetary scanners, and
  - The penetrating scanner normally mounted on Alternate Reality Ultra Stations and Death Stars.
  It does not remove:
  - The Chameleon and Robber Baron scanners unique to Super-Stealth races,
  - The penetrating scanner mounted in Packet Physics races' mineral packets, or
  - The inbuilt penetrating scanner mounted in Jack of all Trades races' Scout, Frigate and Destroyer ships.
  In return, all ordinary scanner ratings are doubled for ships such a race controls (except the organic scanner of AR planets, whose range is multiplied by only SQRT(2), and the scanner of PP mineral packets, whose ordinary rating remains the same). SS, PP and JoaT races receive less points from No Advanced Scanners, as the drawback is much less severe while the benefit remains.
  

• Certain components and abilities allow ships and starbases to become cloaked, making them more difficult to detect. The amount of cloaking a fleet has is shown in-game as a percentage from 0% to 98%. The fundamental equation regarding cloaks and detection through cloaks is:
  
  Scanner range vs. C% cloak = (Scanner range vs. uncloaked ship) * (100% - C%)
  
  So, a ship with a scanning range of 500 ly will only be able to detect an 85%-cloaked fleet at a range of 75 ly or less. Note that ships in orbit of a planet and starbases can only be detected by penetrating scanners, and as such the penetrating scanner range is the one used as "Scanner range vs. uncloaked ship".
  
• A fleet's cloaking percentage is calculated in two stages. The first is the accumulation of "cloak units". Cloaks, and some other components available to Super Stealth races or from the Mystery Trader, provide a ship or starbase a set amount of cloak units per kT mass of the unloaded ship. Starbases of a race with the Improved Starbases lesser racial trait receive a bonus 40 cloak units per kT, and all ships and starbases controlled by a Super-Stealth race (controlled, not built, as with JoaT inbuilt scanners) receive a bonus 300 cloak units per kT (these stack in the case of a Super-Stealth race with Improved Starbases). So, a fleet belonging to a Super-Stealth race containing two 153kT Large Freighters each with two Transport Cloakings (300 cloak units/kT) and two Shadow Shields (70 cloak units/kT) and a 39kT Frigate with two Chameleon Scanners (40 cloak units/kT) would have 2*153*(300+2*300+2*70)+39*(300+2*40) = 333060 cloak units.
  
• The second step is conversion of cloak units into a percentage cloak. The number of cloak units in the fleet is divided by the mass of the fleet in kT (for non-Super-Stealth races, cargo is taken as part of the fleet's mass, reducing cloaking; Super-Stealth races ignore cargo). Then, this is converted into a percentage with the following formula:
  - Let X = the number of cloak units per kT
  - If X is less than or equal to 100, cloak% = X/2
  - If X is between 100 and 300, cloak% = 50 + (X-100)/8
  - If X is between 300 and 612, cloak% = 75 + (X-300)/24
  - If X is between 612 and 1124, cloak% = 88 + (X-612)/64
  - If X is between 1124 and 1379, cloak% = 96
  - If X is between 1380 and 1611, cloak% = 97
  - If X is equal to or greater than 1612, cloak% = 98 (i.e. cloaking is capped at 98%)
  So, to continue the previous example, the fleet has 333060/345 = 965 cloak units/kT, corresponding to a 93% cloak. Note that the cloak unit/kT value of all items that provide them can be reverse-engineered via this formula; for instance, as an Ultra-Stealth Cloak is stated in the technology browser to cloak a ship to 85%, 85 = 75 + (X-300)/24 ∴ X = 540 cloak units/kT.
  
• Cloaks function normally against all ordinary and penetrating scanners, including planetary scanners, PP packet scanning, and JoaT inbuilt hull scanners.
  
• Cloaking is effective against Interstellar Traveller "gate-scanning", with a couple of exceptions. First, the cloaking on the starbase with the stargate can hide the whole planet from a "gate-scan", whereas cloaking a starbase will protect the starbase but not the planet from normal penetrating scanners. Second, there is a known bug causing an IT's 150/600 and any/800 stargates to be unable to detect stargates controlled by a race with Improved Starbases (whether or not they're using the Space Dock and Ultra Station; it's the mere presence of the lesser racial trait that triggers it). Third, cloaking is not effective against the "gate-scanning" of 100/any and any/any stargates, as these have no range limit to reduce.
  
• Cloaking works differently against SD "minefield scanning"; rather than reducing detection range, it reduces the chance of detection. The chance of detecting a cloaked fleet in a minefield is (100% - cloak%). If a cloaked fleet is in more than one SD minefield, each minefield has an independent chance to detect it (for example, a 50%-cloaked fleet in two overlapping minefields would have a 75% overall chance of being detected).
  
• Minefields and wormholes behave in part as though they were cloaked. Minefields and wormholes that are "unknown" can only be detected:
  - if the minefield centre or wormhole is within the range of your planet-penetrating scanners,
  - if the minefield centre or wormhole is within 25% of the range of your ordinary scanners (as though they were 75% cloaked),
  - if one of your ships is actually inside the minefield at the end of the turn (it doesn't need a scanner), or
  - if one of your ships has struck the minefield this turn
  However, if "known", a minefield centre or wormhole can also be detected when simply within range of ordinary scanners (as though they were uncloaked ships in deep space). A minefield or wormhole is flagged as "known" if:
  - you detect it by any of the above means
  - you pass through a wormhole
  Note that the "known" flag persists; even if you lose detection of a minefield or wormhole for several years, or never detected the wormhole exit when passing through it, it will still be more easily detectable in future. There is no known means to reset a minefield to "unknown"; a wormhole is only reset to "unknown" when it jumps.
  
• Wormhole connections (i.e., which pairs of wormhole entrances connect to each other) can only be discovered by passing through them; detecting both ends is not sufficient. Connections will remain visibly apparent on the map view until you lose track of at least one end, at which point they disappear until you rediscover them by passing through them again. An end that jumps will normally be lost in this manner, unless it is reacquired on the same turn it jumps (due to jumping into a location where you can detect even an "unknown" wormhole).
  

• Tachyon Detectors are a special Electrical component available only to Inner-Strength races, which reduce the effectiveness of enemy cloaks. They do this by directly modifying the "cloak%" value in the detection-through-cloaking equation. The formula for this modification is:
  
  Modified cloak% = (Normal cloak%) * (0.95^SQRT(T), minimum 0.81)
  
  where T is the number of Tachyon Detectors affecting the fleet.
  
• Multiple Tachyon Detectors on a single ship stack for the purpose of determining T. Tachyon Detectors on multiple ships within a fleet do not stack, but the highest number of Tachyon Detectors on any ship sets T for the whole fleet. So, a fleet containing a ship with 10 Tachyon Detectors and a Rhino Scanner (50 ly), as well as a ship with only five Tachyon Detectors but a Peerless Scanner (500 ly), will scan as though it had a Peerless Scanner and ten Tachyon Detectors (T = 10, then the modified cloak% and a "scanner range vs. uncloaked ship" value of 500 ly are used in the detection-through-cloaking equation).
  

• Scanner rollover. According to this myth, a 36 Peerless Scanner Nubian with No Advanced Scanners has so much scanning range that it rolls over to 0 and doesn't scan anything. This is false, at least in current versions of Stars!. In my tests in 2.70j RC3 such a scanner Nubian was able to detect ships out to its calculated and stated range of 2448 ly. The AR organic planetary scanner, however, is uncapped, and something weird does seem to happen under extreme overpopulation (1,000,000,000+), but this weirdness may be the fault of Stars! mishandling the population rather than a scanner overflow per se (when I tested this, the 1.14 billion pop I'd dropped on the world grew to 1.16 billion the next turn, then the next turn to a bit over 3 billion which displayed on some of the scanner panes as -1 billion ). In any case, it works normally up to 150 million or so, and it's rare that an AR actually gets a chance to exploit the uncapped scanner to such a ridiculous extent.
  
• Minefield edge detection. According to this myth, once you have detected a minefield having scanning on its edge is sufficient to keep track of it. This is false. While detecting a minefield does become easier once it's been flagged as "known", a scanner still needs to cover the minefield's centre to detect it. A scanner that covers some of the minefield but not the centre does not suffice.

• I've seen people arguing both that NAS is better for detecting minefields/wormholes and that penetrating scanners are better for detecting them. Given that penetrating scan range is about half of ordinary scan range, that NAS doubles ordinary scan range, and that minefields/wormholes are 75% cloaked vs. ordinary scans but uncloaked to penscans, the ultimate answer is that by and large they're about even once decent penetrating scanners appear at Elec 10. If you want a full breakdown:
  - Before penetrating scanners are available, NAS is going to have twice the detection range of non-NAS. Obviously.
  - The Ferret Scanner has a short penetrating range of 50 ly, while NAS races will have 75 ly (Possum) or 112 ly (Gazelle).
  - The Dolphin Scanner has a penetrating range of 100 ly, while NAS races will have 112 ly (Gazelle) or 137 ly (Cheetah).
  - The Elephant Scanner has a penetrating range of 200 ly, while NAS races will have 167 ly (Eagle Eye) or eventually 250 ly (Peerless).
  - Complicating this is that planetary scanners stop improving at Elec 8 for NAS races, while they continue to improve for penscan races. This means that at Elec 10, along with the Dolphin Scanner a non-NAS race is going to have the Snooper 320X planetary scanner and as such 160 ly of minefield detection from their planets. And at maxed Electronics against the NAS Peerless's 250 ly the penscan race also has the Snooper 620X and its 310 ly penscan range.
  
• Keep in mind, when putting scanners on Frigate and Galleon designs, that a second scanner adds only 19% to the first scanner's range. It's often worth it anyway, but not always.

• I made a spreadsheet a few days ago comparing cloak units required to get a given cloaking % and the increase in scanner range required to beat that cloaking %. XAPBob has been kind enough to host it here.
  
• The graph at the top (and another graph to the right of it) plot for every %cloak the cloak units/kT required to achieve that value and the increase in scanner range (or equivalently, scanner number in a picket line) needed to breach that %cloak. For instance, you need 420 cloak units/kT to achieve 80% cloaking, and you need 5x the scanner range to detect it, so there's a point at (420,5). The graphs only differ in that the one on the left uses a logarithmic scale.
  
• The graphs further down plot the total and marginal "efficiency" of various cloaking percentages. The total efficiency is defined as (increase in scanner power required, % of range vs. uncloaked)/(cloak units/kT required). The marginal efficiency is defined as (increase in scanner power required, % of range vs. uncloaked, compared to 1% less cloaking)/(increase in cloak units/kT required, compared to 1% less cloaking).
  
• Follow the blue lines marked "Normal" for now. I'll get to the red lines later.
  
• What can be seen from the efficiency graphs is that there are two rather different "sorts" of cloaking. There's "partial" cloaking, in which you cloak a fleet up to the 50% or 75% breakpoints for a relatively small expenditure, and there's "full" cloaking, in which you use a larger investment to go for 98% or as close to it as you can get. "Full" cloaking is far more efficient in terms of the amount of scanning required to defend equivalently against it, to the point where it becomes infeasible for much of the game for opponents to breach 98% cloaking over any significant distance (a Galleon full of Eagle Eye Scanners only achieves 11 ly range against a 98% cloak). Some awareness o

That is some good stuff. Would you show the how SD field scans work?

Are you sure? I am not arguing, I just seem to remember differently. Something like range instead of probability? Maybe what I remember is having this discussion before.