雷達天文學簡史（一）：兩位開山鼻祖，各有獨門絕技

在科學探索的道路上，有時會出現兩位先行者，各自獨立做出開創性的成果，例如牛頓和萊布尼茨各自創立了微積分，達爾文和華萊士各自提出進化論等等。雷達天文學的濫觴時期也是有兩位開路先鋒，他們是美國的草莽英雄小約翰·H·德威特（John H. DeWitt Jr.）和匈牙利的名門俊傑佐爾坦·拉霍斯·貝（Zoltán Lajos Bay）。

德威特與黛安娜計劃

雷達天文學起步於二戰結束時，最早是軍方組織的。在那個年代，軍方不但有錢，還有大量戰爭時生產的多餘雷達。第一個雷達天文學計劃名為"黛安娜計劃"，領導者是小約翰·H·德威特。

圖一：小約翰·H·德威特。

德威特從小就喜歡玩無線電。1921年，他成為了一名業餘無線電操作員，那時他才十五歲，第二年他就建立了納什維爾的第一個電臺 (Curtis par. 2)。

1940年，德威特在WSM電臺做總工程師。下班時間，除了用自制的射電望遠鏡收聽銀河系的電磁噪音以外，他還經常胡思亂想。一天，他突發奇想，打算用從月球上反射回來的無線電波來研究大氣層。那年5月20號一個月黑風高的夜晚，他用電臺的80瓦發射機嘗試用月球反射138兆赫（波長2米）的無線電波，但由於接收機不夠靈敏而失敗。1942年，他跳槽到貝爾實驗室為海軍設計雷達，之後便入伍，加入美國陸軍通訊兵部隊 (Butrica 6-7)。在部隊中，他還研製了針對迫擊炮的反炮兵雷達 (Curtis par. 2)。

參軍後，他一直對自己的計劃念念不忘。1945年，戰爭一結束他便開始行動。作為埃文斯訊號實驗室（Evans Signal Laboratory）的主管 (Butrica 7)，德威特九月份就組織起了團隊（估計之前就一直在蠢蠢欲動），在新澤西州蒙矛斯堡（Fort Monmouth）開始研究。這個計劃的名字叫"黛安娜計劃"，以羅馬神話中的月亮女神黛安娜命名 (7)。

雖然有軍方的財力支援，但他們並沒有打算設計什麼專用的儀器裝置。天線是從SCR-271雷達上拆下來的。這個32偶極天線被架在一個三十米高塔上，這個高塔只能橫向轉動，因為他們很難弄到更好的東西。這意味著他們只能在月出和月落時進行實驗 (7)。

發射和接收器也都是軍隊已有的。他們選擇了埃德溫·H·阿姆斯特朗（Edwin H. Armstrong，跟登月那人沒親屬關係）為通訊兵部隊設計的晶體發射和接收器，因為晶體能夠提供他們需要的穩定性 (7)。他們使用了112兆赫的頻率，但發射功率只有3000瓦，與今天的行星雷達相比就跟一個電動玩具差不多 (Curtis par. 5)。回波被接收到時會有視覺和聽覺的雙重提示：一個9英寸的陰極射線管和一個180赫茲的嘟嘟聲 (Butrica 7)。

圖二：SCR-271雷達的"彈簧床"天線。

多普勒效應使得返回與發射訊號之間的頻率差距能高達300赫茲 (Butrica 7)，但德威特的團隊依然選擇使用窄頻寬接收器。德威特後來回憶道："我們意識到從月球返回的訊號會非常弱，所以我們必須使用一個頻寬很窄的接收器，這樣才能將雜音降到可以忍受的地步……我們每次都必須將接收器調到一個與發射訊號稍稍不同的頻道——這是地球自轉以及月球的視向速度造成的多普勒效應導致的" (7)。稍後，我們就會看到其他團隊不使用窄頻寬的結果。

經過持續的努力以及崩潰（儀器崩潰，人也崩潰），1946年1月10日早上11點48分，德威特的團隊開始向剛剛升起的月球傳送訊號 (9)。

在無盡的白噪音中，他們等待的每一秒鐘都彷彿是一個永恆。

終於，在11點58分，一個清晰的響聲伴隨著示波器一個微小的波峰出現。他們成功了。12點09分，實驗結束。從新澤西州到月球走一個來回，無線電訊號整整花了2.5秒 (9)。諷刺的是，德威特當時不在場。後來他說："當時我在貝爾馬吃午飯以及在藥店拿一些像香菸之類的東西（1952年戒菸了，感謝上帝）" (9)。

（這說明不戒菸的話容易錯過歷史性時刻。是不是這個道理？）

戰爭部一直等到24號才正式宣佈這次實驗的成功。在此之前，德威特的團隊與研究開發主管範·杜森將軍（General Van Deusen）有了點爭執。範·杜森將軍堅持要在外人確認之後才釋出這次成功，以避免鬧烏龍。於是兩名輻射實驗室的科學家和範·杜森將軍一起見證了一次月出實驗 (9)。

一切準備就緒，儀器狀態良好。在德威特的得力干將，金·斯托多拉的指示下，他們開始向月球發射訊號 (9)。如果沒有差錯，他們三秒鐘後就將收到從月球返回的回波。

然而，什麼都沒有發生。

圖三：德威特後來表示："你們可以想象，我當時感覺要死了" (Butrica 9)。

然後，奇蹟就發生了。一輛大貨車經過，回波立馬就被檢測到了。幾乎所有人都立即歡呼起來，只有範·杜森將軍儘量裝出一副很高興的樣子 (9)。這是雷達天文學以及地-月-地通訊（Earth-Moon-Earth communication）的起源 (Curtis par. 7)。

後來，德威特在通訊兵部隊領導人的要求下改去做導彈預警雷達了。因為沒有可用於測試的導彈，月球便成了替代品。幾年後，通訊兵部隊又為黛安娜計劃建造了一個新的系統，包括一個15米直徑的天線和108兆赫的發射器。這套系統繼續進行月球回聲研究並參與追蹤阿波羅計劃的飛船 (Butrica 9)。

流離失所的佐爾坦·貝

在德威特完成他的實驗後不到一個月，一個匈牙利團隊也成功地完成了這一壯舉。 它的領導者叫做佐爾坦·拉霍斯·貝。

圖四：佐爾坦·拉霍斯·貝。

德威特的最高學歷只有本科，但貝可是以優異的成績在1926年從布達佩斯大學拿到物理博士學位，是學霸中的學霸。在柏林的幾個大學和研究所工作了一段時間後，貝終於成為了匈牙利的塞格德大學（University of Szeged）的理論物理學主席（我猜可能相當於物理系主任）。之後又受邀到通斯拉姆公司（Tungsram，當年是全球第三大燈泡生產商），成為了那裡的工業實驗室負責人。(Butrica 10)

二戰末期，貝對電離層很感興趣。根據當時的假說，短波無線電波能夠穿過電離層，而不是像大部分的無線電波一樣被電離層反射。然而，還沒有人驗證過這一假說 (Bay 1)。這時，貝就想到用月球作為一個反射面，看看短波無線電波能不能穿過電離層並被反射回來。

貝使用的儀器引數與德威特非常相似。他們都使用了3000瓦功率的發射器，頻率也幾乎一樣 (Bay 3; Curtis par. 5)。他們也面對著同一個問題：噪音。

由於從月球反射回來的訊號實在太弱，聲噪比就會十分誇張。根據貝的計算，如果不做任何改善，聲噪比η=3.9·10-4 (Bay 4)，也就是說，噪音是聲音的三萬九千倍！這就好像要在飛機起飛的噪音下聽清跑道上一隻蚊子的嗡嗡聲。

德威特的解決方案是縮窄頻寬，這樣會接收到更少的噪音 (DeWitt 233)（在無線電中，頻寬是指訊號的頻率範圍。由於天氣、目標材質或儀器精度等問題，訊號頻率可能會出現偏差。為了確保接收到訊號，接收器便會接收更大的頻率範圍）。貝也知道這一點。在他的計算中，如果縮窄頻寬的話，聲噪比η能一下子提高到3.6（也就是說聲音比噪音要大3.6倍）(Bay 5)，聽到訊號簡直輕而易舉。

然而，德威特能夠縮窄頻寬是因為他在發射和接收器中都使用了晶體，這能夠很有效地保證訊號頻率的穩定 (DeWitt 233)。但是，貝以及他的團隊沒有這種裝置。

你以為貝會放棄？不存在的！貝可是名優秀的物理學家，而且動手能力極強。他用一種天才的辦法解決了這一問題，而他的解決方案在很多領域一直沿用至今。

圖五：貝的裝置。

貝使用了幾個庫倫表（又稱電量計）。有電流透過時，這些庫倫表會將自己管中的水電解，在圖五所示的小管子裡累積氫氣，這些氫氣就表示透過這一表的電荷量。這些庫倫表被連線在一個旋轉開關上，這開關就會輪流給每個庫倫表通電，3秒輪迴一次。這些電就是接收器接收到的無線電訊號(Butrica 10-11)。

由於極低的聲噪比，每個庫倫表接收到的電荷量幾乎一樣，主要都是噪聲。然而，由於訊號的發射是週期性的，訊號每次返回時都會通到同一個庫倫表上。久而久之，這個庫倫表中就會記錄下更多的電荷，貝的團隊就可以從這裡得知他們的確是收到從月球上反射回來的訊號了 (Butrica 11; Harrison par. 1)。

這是一個天才的主意。一直到現在，貝的這種方法依然是雷達天文學中的一個重要手段，是之後雷達探測金星和其他天體的堅實基礎 (Butrica 12)。然而，再好的主意也需要實施的機會。二戰時期，匈牙利被納粹德國佔領。到戰爭末期，德國節節敗退時，布達佩斯不斷地被盟軍轟炸，之後又發生了激烈的布達佩斯包圍戰，貝被迫隨著通斯拉姆公司的實驗室撤離到郊外 (11)。

直到二戰結束，貝才得以實施他的計劃。通斯拉姆的實驗室太吵，干擾嚴重，所以貝的團隊只能在黃昏和晚上進行實驗（不知道發不發加班費）(11)。如果沒有戰爭的干擾，貝很有可能在德威特之前成為第一個用月球反射無線電波的人。

德威特和貝都是雷達天文學的先行者。與他們同時期還有許多別的團隊也在使用雷達進行別的研究，如研究流星對大氣的電離 (12-13)。然而，當時他們並沒有掀起什麼波瀾。根據德威特的成果，戰爭部預言以後會有"對月球和其他行星的精確地圖繪製、對電離層的測量和分析、以及從地面用無線電控制在平流層以上環繞地球的太空船和噴氣或火箭發動機控制的導彈" (9)。然而，《新聞週刊》（對，就叫這個，英文是Newsweek）稱這簡直是凡爾納的幻想 (9)。雷達天文學真正起飛還要等到1958年後。

我們下次再見。

——劉騰駿

參考資料：

Bay, Z. Reflection of microwaves from the Moon. Hungarica Acta Physica 1, 1–22 (1947). https://doi.org/10.1007/BF03161123.

Butrica, Andrew J. “To See the Unseen—A History of Planetary Radar Astronomy.” NASA History Office, 1996, https://history.nasa.gov/SP-4218/sp4218.htm.

Curtis, Anthony R. “Space&Beyond: Moonbounce Advances the State of the Radio Art.” ARRLWeb: Space&Beyond: Moonbounce Advances the State of the Radio Art, 21 Jan. 2002, web.archive.org/web/20071025022111/www2.arrl.org/news/features/2002/01/21/1/.

DeWitt, John H, and E. K. Stodola. “Detection of Radio Signals Reflected from the Moon.” Proceedings of the IRE, vol. 37, no. 3, Mar. 1949, pp. 229–242., doi:10.1109/jrproc.1949.231276.

Harrison, Todd. “RETROTECHTACULAR: [ZOLTÁN BAY’S] MOON BOUNCE COULOMETER SIGNAL AMPLIFIER.” Hackaday, 19 Nov. 2013, hackaday.com/2013/11/19/retrotechtacular-zoltan-bays-moon-bounce-coulometer-signal-amplifier/.

圖片：

圖一：Mofenson, Jack. “Lt. Colonel John H. DeWitt Jr., in Charge of the Project, a Modified Version of the SCR-271 Early-Warning Radar Used at Pearl Harbor. DeWitt Is the Former Chief Engineer of WSM.” Radar Echoes From the Moon, Belmar, New Jersey, Jan. 1946, web.archive.org/web/20081029000712/http://www.eagle.ca/~harry/ba/eme/index.htm.

圖二：Butrica, Andrew J. “To See the Unseen—A History of Planetary Radar Astronomy.” NASA History Office, 1996, https://history.nasa.gov/SP-4218/sp4218.htm.

圖四："File:Zoltán Bay (1900-1992) Hungarian physicist.jpg." Wikimedia Commons, the free media repository. 31 Oct 2020, 05:47 UTC. 6 Jan 2021, 14:26 <https://commons.wikimedia.org/w/index.php?title=File:Zolt%C3%A1n_Bay_(1900-1992)_Hungarian_physicist.jpg&oldid=508227919>.

圖五：Bay, Z. Reflection of microwaves from the Moon. Hungarica Acta Physica 1, 1–22 (1947). https://doi.org/10.1007/BF03161123.

The history of Radar Astronomy (I): De la Terre à la Lune, trajet et retour direct en 2.5 secondes

On the path of scientific discovery, we occasionally see not one, but a pair of pioneers, each independently producing groundbreaking results. We saw Newton and Leibniz independently developing calculus while Darwin and Wallace each separately created their theory of evolution. In the early years of radar astronomy, we also saw a pair of trailblazers. One was the American engineer and astronomer John H. DeWitt Jr. and the other was Hungarian physicist Zoltán Lajos Bay.

DeWitt and Project Diana

Radar astronomy can trace its origins back to the end of the Second World War. It was organised by the military because the military not only had adequate funding but also large amounts of surplus radars produced during the war. The first radar astronomy project was named "Project Diana". Its leader was John H. DeWitt Jr.

Fig. 1: John H. DeWitt Jr.

DeWitt had been playing with the radio since childhood. In 1921, he became an amateur radio operator at the age of fifteen. He built Nashville's first radio station the next year (Curtis par. 2).

In 1940, DeWitt was the chief engineer for the radio station WSM. In his free time, apart from listening to radio noise from the Milky Way using a radio telescope he made himself, he also came up with lots of wild ideas. One day, DeWitt had a new idea: using radio waves reflected off the moon to investigate the atmosphere. That same year, on the 20th of May, he used the radio station's 80-watt transmitter to reflect a 138 megahertz (2-metre wavelength) off the moon, but his receiver wasn't sensitive enough. In 1942, DeWitt joined Bell Labs to design radars for the navy. He was later commissioned in the United States Signal Corps (Butrica 6-7). While there, he designed counter-battery radar for mortars (Curtis par. 2).

DeWitt never forgot his plan. When the war ended in 1945, he took action. As the director of the Evans Signal Laboratory (Butrica 7), DeWitt assembled a team by September (he probably had been secretly plotting for a while) and began research at Fort Monmouth in New Jersey. The project was called "Project Diana", named after the Roman moon goddess Diana (7).

Although they had military backing, DeWitt's team did not use any purpose-built equipment. Their aerial was from an SCR-271 radar. This 32-dipole antenna was mounted on a 30-metre tower. The tower could only turn sideways as it was too difficult to acquire anything better. This meant that they could only experiment at moonrise and moonset (7).

The military had ready-made transmitters and receivers. They chose a crystal transmitter and receiver which Edwin H. Armstrong designed for the Signal Corps, as the crystal provides the stability they needed (7). They chose a frequency of 112 megahertz, but their transmitting power was only 3000 watts, toys compared to today's planetary radars (Curtis par. 5). Reception of signals was signified by both visual and audial notifications: a 9-inch cathode ray tube and a 180-hertz beep (Butrica 7).

Fig. 2: SCR-271 radar's "spring bed" antenna.

The Doppler effect caused differences in frequency between the transmitted and received signal to be as much as 300 hertz (Butrica 7), but DeWitt's team still decided to use a narrow bandwidth receiver. DeWitt later recalled: "We realized that the moon echoes would be very weak so we had to use a very narrow receiver bandwidth to reduce thermal noise to tolerable levels… We had to tune the receiver each time for a slightly different frequency from that sent out because of the Doppler shift due to the earth's rotation and the radial velocity of the moon at the time" (7). We shall soon see the result of other groups not using a narrow bandwidth in such experiments.

After continuous effort and breakdowns (possibly both technical and mental), at 11:48 a.m. on the 10th of January 1946, DeWitt's team began transmitting signals to the rising moon (9).

Sitting in the endless sea of white noise, every second they waited was an eternity.

Finally, at 11:58, a crisp beep accompanied by a minuscule but distinct peak appeared. They succeeded. At 12:09, the experiment ended. A round trip from New Jersey to the moon and back took the radio signal 2.5 seconds (9). Ironically, DeWitt wasn't present. He later said: "I was over in Belmar having lunch and picking up some items like cigarettes at the drug store (stopped smoking 1952 thank God)" (9).

(This shows that if you don't quit smoking, you might miss historic events. Get it?)

The War Department withheld the news of success until the 24th. Before that, DeWitt and his team had a bit of trouble with the head of R&D, General Van Deusen. General Van Deusen insisted that the results should be checked by outsiders before being announced, so two scientists from the Radiation Laboratory and General Van Deusen observed a moonrise experiment (9).

Everything was ready. Under the instruction of DeWitt's best employee, King Stodola (who is not the king of anywhere except the realm of science), the team began transmitting signals to the moon (9). If nothing went wrong, they should start to hear echoes after about 3 seconds.

However, nothing happened.

DeWitt later said: "You can imagine that at this point I was dying" (Butrica 9).

Then, a miracle. A big truck passed by, and the echoes immediately popped up. Almost everyone cheered; only General Van Deusen tried his best to look pleased (9). This was the very beginning of radar astronomy and Earth-Moon-Earth communication (Curtis par. 7).

Later, DeWitt was ordered to develop missile warning radars. Because there weren't any missiles available for testing, the moon became a substitute. Several years later, the Signal Corps built a new system for Project Diana, including a 15-metre diameter antenna and a 108 megahertz transmitter. This system continued to conduct moon echo research and took part in tracking the Apollo spacecraft (Butrica 9).

Zoltán Bay: the scientist on the move

Less than a month after DeWitt concluded his experiment, a Hungarian team replicated his results. The team's leader was Zoltán Lajos Bay.

Fig. 3: Zoltán Lajos Bay.

DeWitt only had a bachelor's degree, but Bay graduated with highest honours from the University of Budapest with a PhD in physics in 1926. After working at several universities and research institutes in Berlin, Bay finally became the Chair of Theoretical Physics at the University of Szeged. Later, he was invited by Tungsram (the then third-largest producer of lightbulbs in the world) to head Tungsram's industrial laboratory (Butrica 10).

In the last stages of World War Two, Bay became interested in the ionosphere. According to hypothesis, short wave radio waves should be able to penetrate the ionosphere, unlike most radio waves which were reflected. However, no one had been able to verify the hypothesis (Bay 1). Bay realised that he could use the moon as a reflector to see if short wave radio waves could pass through the ionosphere and be reflected.

The equipment Bay used was very similar to those used by DeWitt. They both used a 3000-watt transmitter and almost the same frequency (Bay 3; Curtis par. 5). They also faced the same problem: noise.

Because the echoes returning from the moon were too weak, the signal-to-noise ratio was terrible. According to Bay's calculations, if nothing was done to improve the ratio, it would be equal to 3.9·10^-4 (Bay 4). In other words, the noise would be thirty-nine thousand times louder than the echo! This is like trying to hear the buzzing of a mosquito on a runway where a plane is taking-off.

DeWitt's solution was to narrow the bandwidth so that they received less noise (DeWitt 233) (in signal processing, bandwidth refers to the range of frequencies a signal contains. Due to issues such as the weather, target material or equipment precision, the signal's frequency may shift. To ensure the reception of the signal, the receiver usually tries to receive a larger number of bandwidths). Bay also knew this. In his calculations, he found that if he narrowed the bandwidth, the signal-to-noise ratio would instantly rise to 3.6 (or in other words, the signal would be 3.6 times louder than the noise) (Bay 5). Hearing the echoes would be a piece of cake.

However, the reason DeWitt was able to narrow his bandwidth was that he used crystals in both his transmitter and receiver, which ensured the stability of the signal (DeWitt 233). But Bay and his team did not have such equipment.

You thought Bay would give up? Of course not! Bay was a brilliant physicist with an equally brilliant hands-on ability. He created a genius solution, one which was used to this day.

Fig. 4: Bay's apparatus.

Bay used several coulometers. When a current passed through, these coulometers electrolysed the water in their tube, causing hydrogen to accumulate in the small tubes shown in Fig. 4. The hydrogen indicated the amount of electric charge which passed through the coulometer. These coulometers were connected to a rotating switch. The switch passed electric current alternately into each of the coulometers, finishing every sweep in 3 seconds. The current came from the radio signals received by the receiver (Butrica 10-11).

Due to the extremely low signal-to-noise ratio, every coulometer received almost the same amount of electric charge, mostly noise. However, because the signals were sent periodically, the received echo will pass through the same coulometer every time. After a while, this coulometer will record more electric charge, allowing Bay's team to know that they had received signals from the moon (Butrica 11; Harrison par. 1).

This was a stroke of genius. Even today, Bay's method is still an important tool in radar astronomy. It was the foundation for the radar imaging of Venus and other planets (Butrica 12). Nevertheless, even the most brilliant of ideas need a chance to be applied. During World War Two, Hungary was occupied by Nazi Germany. In the last stages of the war, while Germany was on the retreat, Budapest was constantly bombed by the Allies. Later, the fierce Siege of Budapest occurred. Bay was forced to move into the countryside with Tungsram's industrial laboratory (11).

Only until the war ended when Bay was able to carry out his plan. Tungsram's laboratory was too noisy. The interference was so bad that Bay's team had to do measurements at dusk or at night (I wonder if they received overtime pay) (11). Without the war, Bay could have become the first person to bounce radio waves off the moon.

DeWitt and Bay were both pioneers in radar astronomy. Many other teams also used radar in research, like investigating the ionisation of the atmosphere by meteors (12-13). That said, there was no revolution around the world. According to DeWitt's results, the War Department predicted that there would be "the accurate topographical mapping of the Moon and planets, measurement and analysis of the ionosphere, and radio control from Earth of 'space ships' and 'jet or rocket-controlled missiles, circling the Earth above the stratosphere'" (9). However, Newsweek called these predictions "worthy of Jules Verne" (9). Radar astronomy would only take off after 1958.

See you next time.

——Tengjun Liu

Citations:

Bay, Z. Reflection of microwaves from the Moon. Hungarica Acta Physica 1, 1–22 (1947). https://doi.org/10.1007/BF03161123.

Butrica, Andrew J. “To See the Unseen—A History of Planetary Radar Astronomy.” NASA History Office, 1996, https://history.nasa.gov/SP-4218/sp4218.htm.

Curtis, Anthony R. “Space&Beyond: Moonbounce Advances the State of the Radio Art.” ARRLWeb: Space&Beyond: Moonbounce Advances the State of the Radio Art, 21 Jan. 2002, web.archive.org/web/20071025022111/www2.arrl.org/news/features/2002/01/21/1/.

DeWitt, John H, and E. K. Stodola. “Detection of Radio Signals Reflected from the Moon.” Proceedings of the IRE, vol. 37, no. 3, Mar. 1949, pp. 229–242., doi:10.1109/jrproc.1949.231276.

Harrison, Todd. “RETROTECHTACULAR: [ZOLTÁN BAY’S] MOON BOUNCE COULOMETER SIGNAL AMPLIFIER.” Hackaday, 19 Nov. 2013, hackaday.com/2013/11/19/retrotechtacular-zoltan-bays-moon-bounce-coulometer-signal-amplifier/.

Images:

Fig. 1: Mofenson, Jack. “Lt. Colonel John H. DeWitt Jr., in Charge of the Project, a Modified Version of the SCR-271 Early-Warning Radar Used at Pearl Harbor. DeWitt Is the Former Chief Engineer of WSM.” Radar Echoes From the Moon, Belmar, New Jersey, Jan. 1946, web.archive.org/web/20081029000712/http://www.eagle.ca/~harry/ba/eme/index.htm.

Fig. 2: Butrica, Andrew J. “To See the Unseen—A History of Planetary Radar Astronomy.” NASA History Office, 1996, https://history.nasa.gov/SP-4218/sp4218.htm.

Fig. 3: "File:Zoltán Bay (1900-1992) Hungarian physicist.jpg." Wikimedia Commons, the free media repository. 31 Oct 2020, 05:47 UTC. 6 Jan 2021, 14:26 <https://commons.wikimedia.org/w/index.php?title=File:Zolt%C3%A1n_Bay_(1900-1992)_Hungarian_physicist.jpg&oldid=508227919>.

Fig. 4: Bay, Z. Reflection of microwaves from the Moon. Hungarica Acta Physica 1, 1–22 (1947). https://doi.org/10.1007/BF03161123.